48. To study the dependence of the potential difference across a resistor on the current through it and to determine its resistance and to verify Ohm’s law.
Aim:
To study the dependence of the potential difference across a resistor on the current through it and to determine its resistance and to verify Ohm’s law.
Theory
According to Ohm’s law, the potential difference (V) across the ends of a resistor is directly proportional to the current (I) through it provided its temperature remains the same. That is
V∝I
or
V/I = constant = R
or V = RI
Here R is a constant for the given resistor at a given temperature and is called its resistance. The SI unit of resistance is ohm (W). A graph between the potential difference across the two ends of a resistor and the current through it is a straight line passing through the origin. The slope of this graph gives the resistance R of the resistor.
To verify Ohm’s law, we measure the potential difference across the two ends of a resistor at different currents through it in an electric circuit. The current through the resistor is measured by connecting an ammeter in series with it. The potential difference across the two ends of the resistor is measured by connecting the voltmeter in parallel with it. A straight line graph obtained between V and I verifies Ohm’s law.
Materials Required
A resistor of about 5 Ω, an ammeter ( 0 - 3 A), a voltmeter (0 - 10 V), four dry cells of 1.5 V each with a cell holder (or a battery eliminator), a plug key, connecting wires, and a piece of sandpaper.
Procedure
- Note the range and least count of the given ammeter and the voltmeter.
- Fresh connecting wires have an insulating layer on them. Similarly, the connecting wires lying unused for some time may also develop an insulating layer. (How?) It is therefore important to clean the ends of connecting wires using sandpaper.
- Draw a circuit diagram for studying Ohm’s law as shown in Fig. 48.1 in your notebook. Observe how different components like the ammeter, voltmeter, resistor, and plug key are connected with the cells (or battery eliminator).
- Set up the circuit by connecting different components with the help of connecting wires.
- Initially connect only one cell in the circuit (that is, make cell connections between points A and B). In case a battery eliminator is used, keep the rating of the eliminator at the minimum (say at 2 V).

- Make sure that the positive and negative terminals of the ammeter and voltmeter are correctly connected in the circuit as shown in Fig. 48.1. Get the circuit set up by you and checked by the teacher before inserting the key into the plug.
- Insert the key in the plug to let the current establish in the circuit. Note the readings of the ammeter and voltmeter and record them. The voltmeter measures the potential difference (V) across the two ends X and Y of the resistor, and the ammeter measures the current I through it. Remove the key from the plug to avoid unnecessary heating of wires. How does it happen? Think it by the Joule’s law of heating.)
- Now instead of using one cell in the circuit, connect two cells in the circuit (that is, make cell connections between points A and C); in case a battery eliminator is used, increase its rating. Insert the key in the circuit. Note and record the voltmeter and ammeter readings.
- Repeat the experiment by connecting three and four cells in the circuit.
Observations and Calculations
(i) Range of the ammeter = ___ - ___ A.
(ii) Least count of the ammeter = ___ A.
(iii) Range of the voltmeter = ___ − ___ V.
(iv) Least count of the voltmeter = ___ V.
The mean value of resistance R of the resistor = _____ Ω

Graph
Find the range of variation in the values of I and V. Choose appropriate scales for the I and V along the x- and y-axes, respectively, on the graph paper. Mark the points on the graph paper for each value of current I and corresponding value of potential difference V (Fig. 48.2). Join all the points as a smooth line as possible, such that most of the points lie on it. Find the slope of this straight-line graph by choosing two points P and Q. This slope is the resistance of the resistor used in the circuit (Fig. 48.1).

slope= QM/MP

Extend the straight line of the graph backwards to check whether it meets the origin of the graph paper.
Results and Discussion
- Compare the value of resistance R of the resistor obtained from the calculations (as given in the observation table) and obtained from the graph.
- The value of resistance R of the resistor for all values of current through it remains the same (or almost the same). The graph between V and I is a straight line and passes through the origin. This verifies Ohm’s law.
Precautions and sources of error
- The connecting wires should be thick copper wires, and the insulation of their ends should be removed using sandpaper.
- Connections should be tight; otherwise, some external resistance may introduce in the circuit.
- The ammeter should be connected in series with the resistor such that the current enters at the positive terminal and leaves at the negative terminal of the ammeter.
- A voltmeter should always be connected in parallel to a resistor. The pointers of the ammeter and voltmeter should be at the zero mark when no current passes through the circuit. If not, then ask your teacher to correct it.
- Current should be passed through the circuit for a short time while taking observations; otherwise, current would cause unnecessary heating in the circuit. Heating may change the resistance of resistors.
Note for the Teacher
- If a resistor of known resistance is not available, a piece of nichrome wire of suitable length may also be used.
- In place of dry cells, Leclanche and Daniel cells can be used. A battery eliminator may also be used. In case a battery eliminator is used, it is suggested to guide students accordingly while connecting it to the circuit and taking observations.
- If an accumulator or battery is used in place of cells or an eliminator to draw the current in the circuit, then a rheostat or variable resistance box can be used to change the current flowing through the circuit.
- In case your school laboratory possesses the voltmeter and ammeter of ranges other than the prescribed ranges, then the resistors may be so chosen that an appreciable deflection may appear in the ammeter and voltmeter.
Questions
- In this experiment, it is advised to take out the key from the plug when the observations are not being taken. Why?
- Suppose the ammeter (or voltmeter) you are using in this experiment does not have positive (+) and negative (-) terminal markings. How will you use such an ammeter (or voltmeter) in the circuit?
- If the resistor of a known resistance value is replaced with a nichrome wire of 10 cm length (say). How do the values of current through the nichrome wire and potential difference across the two ends of it change? How will the values change if the replaced wire is of manganin in place of nichrome?
- Suppose in this experiment you see that the deflection on the ammeter (or voltmeter) scale goes beyond the full scale. What will you infer from such an observation? What will you infer if the deflection takes place in the opposite direction?
- Why is it advised to clean the ends of connecting wires before connecting them?
49. To study the factors that affect the resistance of a resistor.
Aim:
To study the factors that affect the resistance of a resistor.
Theory
On applying Ohm’s law, it is observed that the resistance of a resistor depends on its length, on its area of cross-section and on the nature of its material. Precise measurements have shown that the resistance (R) of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A). That is,
R ∝ l and
R ∝ 1/A. Thus R = ρ (l/A) (1)
Here ρ is a constant of proportionality and is called the electrical resistivity of the material of the conductor. The SI unit of resistivity is the ohm meter (Ωm). In this experiment, we study these factors in an electric circuit by employing different resistors (wires) of different lengths and areas of crosssection. Using Ohm’s law, the resistance of a conductor in an electric circuit can be determined by measuring the current through it and the potential difference across its ends. An ammeter (connected in series with the resistor) measures the current through it, and a voltmeter (connected parallelly with the resistor) measures the potential difference across its two ends.
Materials Required
Two SWG-20 (standard wire gauge) constantan (or manganin) wires of lengths 10 cm and 20 cm respectively, one SWG-24 constantan (or manganin) wire of 10 cm length, one SWG-20 (or SWG-24) nichrome wire of 10 cm length (all wires must be attached with the connectors at both ends, such as crocodile clips), an ammeter (range 0–500 mA), a voltmeter (range 0–5 V), four dry cells of 1.5 V each with a cell holder (or a battery eliminator), a plug key, crocodile clips, connecting wires, and a piece of sandpaper. The area of the cross-section of a SWG-20 wire is 5.178 × 10-7 m2, and the area of the cross-section of a SWG-24 wire is 2.05 × 10-7 m2.
Procedure
- Note the range and least count of the given ammeter and the voltmeter.
- Fresh connecting wires have an insulating layer at the top. Similarly, the connecting wires lying unused for some time may also develop an insulating layer. (How?) It is therefore important to clean the ends of connecting wires using sandpaper.
- Draw a circuit diagram for studying the factors that affect the resistance of a resistor, as shown in Fig. 49.1 in your notebook. Observe how different components like the ammeter, voltmeter, and plug key are connected with the cells or battery eliminator. Note that a resistor is to be connected in the circuit between points A and B.

- Set up the circuit by connecting different components with the help of connecting wires. Connect all four cells in the circuit. In case a battery eliminator is used, keep the rating of the eliminator at about 6 V.
- Label the given wires (resistors) as follows: SWG-20 constantan (or manganin) wire of length 10 cm as wire 1, SWG 20 constantan (or manganin) wire of length 20 cm as wire

- 2, SWG-24 constantan (or manganin) wire of length 10 cm as wire 3, and SWG-20 (or SWG-24) nichrome wire of length 10 cm as wire 4.
All the wires must be attached to connectors such as crocodile clips, as shown in Fig. 49.1(b). This will ensure that the entire length of the wire will come into the circuit as a resistor.
- Connect wire 1 between points A and B. Make sure that the positive and negative terminals of the ammeter and voltmeter are correctly connected in the circuit as shown in Fig. 49.1. Get the circuit checked by the teacher before inserting the key into the plug.
- Insert the key in the plug to let the current establish in the circuit. Note the readings of the ammeter and voltmeter and record them. Ensure that the key is removed from the plug just after taking the ammeter and voltmeter readings to avoid unnecessary heating of wires.
- Now replace wire 1 by wire 2. Insert the key in the plug, measure the current through wire 2, and measure the potential difference across the ends of wire 2. Notice the difference in the values of current and potential differences. Remove the key.
- Repeat step 8 for wires 3 and 4.
Observations and Calculations
(i) Range of the ammeter = ___ - ___ A.
(ii) Least count of the ammeter = ___ A.
(iii) Range of the voltmeter = ___ − ___ V.
(iv) Least count of the voltmeter = ___ V.

Results and Discussion
Infer about the factors that affect the resistance of a resistor and answer the following:
- How does it change with length?
- How does it change with the area of the cross-section?
- How does it change with the resistivity of the material of the wire? (Get the resistivity of the materials from the textbook/Appendix-I.)
Precautions
- The connecting wires should be thick copper wires, and the insulation of their ends should be removed using sandpaper.
- Connections should be tight; otherwise, some external resistance may be introduced in the circuit.
- The ammeter should be connected in series with the resistor such that the current enters at the positive terminal and leaves at the negative terminal of the ammeter.
- The voltmeter should always be connected in parallel to the resistor.
- The pointers of the ammeter and voltmeter should be at the zero mark when no current is flowing through the circuit. If not, then ask your teacher to correct it.
- Current should be passed through the circuit for a short time while taking observations; otherwise, current would cause unnecessary heating in the circuit. Heating may change the resistance of resistors.
Note for the Teacher
- The number of cells to be used in the circuit is not fixed. The number of cells or the rating of the battery eliminator will, however, depend on the wires to be used as resistors in the circuit to give an appreciable amount of current to be measured by the ammeter.
- In place of dry cells, a battery eliminator or a 9 V battery may be used. In case a battery eliminator is used, it is suggested to guide students accordingly while connecting it to the circuit and taking observations.
- In case your school laboratory possesses the voltmeter and ammeter of ranges other than the prescribed ranges, then the resistors may be chosen such that an appreciable deflection may appear on the ammeter and voltmeter scales.
- In this experiment, it is suggested to use SWG-20 and SWG-24 constantan (or manganin) and nichrome wires. However, this is suggestive and not mandatory. In case these are not available, other wires may also be used. It is suggested that the choice of wires should be judicious to get an appreciable deflection on the scales of the ammeter and voltmeter available in the laboratory. Further, the area of the cross-section of each wire should also be provided to the students. Appendix J may be consulted for this purpose. In case the standard wire gauge of the wires is not known, the diameter of the wire may be determined using a screw gauge.
Questions
- A thick and thin wire of the same length and material are connected to the same source. Which of the two will draw more current from the source?
- A copper wire is stretched uniformly to double its length; how will its resistance change? Will its resistivity also be changed?
- What happens to the value of current if the positions of battery and ammeter are interchanged in such a manner that the current enters at the positive terminal of the ammeter?
- On what factors does the resistance of a conductor depend?
- If the plug key is interchanged by the ammeter in this experiment, would you be able to experiment?
50. To determine the equivalent resistance of two resistors connected in a series combination.
Aim:
To determine the equivalent resistance of two resistors connected in series combination.
Theory
When two resistors of resistance R1 and R2 respectively are connected in a series combination (Fig. 50.1), then their equivalent resistance Rs is given by
Rs = R1 + R2. — —(1)

In order to determine the resistance of a combination of resistors in series, the current I flowing through the circuit is measured with an ammeter connected in series with the combination. The potential difference V across the combination of resistors is measured with a voltmeter connected in parallel (Fig. 50.2).
Materials Required
Two resistors of (each of 2 Ω resistance), an ammeter (range 0–5 A), a voltmeter (range 0–5 V), three dry cells of 1.5 V each with a cell holder (or a battery eliminator), a plug key, connecting wires, and a piece of sandpaper.
Procedure
- Note the range and least count of the given ammeter and the voltmeter.
- Fresh connecting wires also have an insulating enamel layer at the top. Similarly, the connecting wires lying unused for some time may also develop an insulating layer.
- (How?) It is therefore important to clean the ends of connecting wires using sandpaper.
- Draw a circuit diagram for the series combination of resistors as shown in Fig. 50.2 in your notebook. Observe how different components like the ammeter, voltmeter, combination of resistors in series (of known resistances R1 and R2), and the plug key are connected with the cell(s) (or battery eliminator).
- Place the given resistors one after the other and join the ends labelled B and C as shown in Fig. 50.1. Set up the circuit by connecting different components with the help of connecting wires as shown in the circuit diagram.
- Make sure that the positive and negative terminals of the ammeter and voltmeter are correctly connected in the circuit as shown in Fig. 50.2. Get the circuit set up by you checked by the teacher before inserting the key into the plug.
- Insert the key in the plug to let the current establish in the circuit. Note the readings of the ammeter and voltmeter and record them. The voltmeter measures the potential difference (V) across the two ends A and D of the series combination of two resistors, and the ammeter measures the current I through the series combination. Remove the key from the plug to avoid unnecessary heating of wires. How does it happen? Think of it in accordance with Joule’s law of heating.)
- Repeat the activity for three different values of current through the circuit and record the readings of the ammeter and voltmeter in each case. The current through the circuit may either be decreased or increased by changing the number of cells in the circuit (or by changing the settings of the battery eliminator terminal).
Observations and Calculations
Range of the ammeter = ___ - ___ A.
Least count of the ammeter = ___ A.
Range of the voltmeter = ___ - ___ V.
Least count of the voltmeter = ___ V.
Resistance of first resistor R1 = ___ Ω.
Resistance of second resistor, R2 = ___ Ω.

R1 = ____ Ω, R2 = _____ Ω
Equivalent resistance [from Eq. (1)] = R1 + R2 = ___ Ω
Results and Discussion
Compare the observed value of the equivalent resistance of the series combination of the two given resistors (from the observation table) with the calculated value of it using Eq. (1).
Precautions
- The connecting wires should be thick copper wires, and the insulation of their ends should be removed using sandpaper.
- Connections should be tight; otherwise, some external resistance may be introduced in the circuit.
- The ammeter should be connected in series with the combination of resistors such that the current enters at the positive terminal and leaves at the negative terminal of the ammeter.
- The voltmeter should always be connected in parallel to the combination of resistors.
- The pointers of the ammeter and voltmeter should be at the zero mark when no current flows through the circuit. If not, then ask your teacher to correct it.
- Current should be passed through the circuit for a short time while taking observations; otherwise, current would cause unnecessary heating in the circuit. Heating may change the resistance of resistors.
Note for the Teacher
- The internal resistance of cells should be much lower than the resistance of external resistors used in the experiment.
- In case an accumulator or battery is used in place of cells or an eliminator to draw the current in the circuit, then a rheostat or variable resistance box can be used to change the current flowing through the circuit.
- In case your school laboratory possesses the voltmeter and ammeter of ranges other than the prescribed ranges, then the resistors may be chosen such that an appreciable deflection may appear in the ammeter and voltmeter.
Questions
- If two resistors having resistances of 2 Ω and 4 Ω, respectively, are connected in a series combination in an electric circuit, what will be the net resistance in the circuit?
- In an electric circuit, a resistor of 5Ω resistance is connected to a battery (5 V) through an ammeter and a plug key. Now in this circuit, another resistor of 10 Ω is connected in series with the 5 Ω resistor. Will there be any change in the ammeter reading? How much?
- In the above question, what is the potential difference across the two ends of the resistor of 5Ω resistance when it is alone in the circuit? What is the potential difference across the two ends of a resistor of 5Ω resistance when it is connected in series with the resistor of 10Ω resistance? What is the potential difference across the series combination?
51. To determine the equivalent resistance of two resistors connected in parallel combination.
Aim:
To determine the equivalent resistance of two resistors connected in parallel combination.
Theory
When two resistors of resistance R1 and R2 respectively are connected in a parallel combination (Fig. 51.1), then their equivalent resistance Rp is given by

In order to determine the resistance of a combination of resistors connected in parallel, the current I flowing through the circuit is measured with an ammeter connected in series with the combination. The potential difference V across the combination of resistors is measured with a voltmeter connected in parallel (Fig. 51.2).


Materials Required
Two resistors of (each of 2Ω resistance), an ammeter (range 0–5 A), a voltmeter (range 0–5 V), three dry cells of 1.5 V each with a cell holder (or a battery eliminator), a plug key, connecting wires, and a piece of sand paper.
Procedure
- Note the range and least count of the given ammeter and the voltemeter.
- Fresh connecting wires also have an insulating enamel layer at the top. Similarly, the connecting wires lying unused for some time may also develop an insulating layer. (How?) It is therefore important to clean the ends of connecting wires using sandpaper.
- Draw a circuit diagram for the series combination of resistors as shown in Fig. 51.2 in your notebook. Observe how different components like the ammeter, voltmeter, combination of resistors in parallel (of resistances R1 and R2), and the plug key are connected with the cell(s) (or battery eliminator).
- Place the given resistors side by side and join end A with end C and end B with end D (Fig. 51.1). Set up the circuit by connecting different components with the help of connecting wires as shown in the circuit diagram (Fig. 51.2).
- Make sure that the positive and negative terminals of the ammeter and voltmeter are correctly connected in the circuit. Get the circuit set up checked by the teacher before inserting the key into the plug.
- Insert the key in the plug to let the current establish in the circuit. Note the readings of the ammeter and voltmeter and record them. The voltmeter measures the potential difference (V) across the two Fig. 51.2: Circuit diagram for the series combination of two resistors AB and CD ends A and D of the series combination of two resistors, and the ammeter measures the current I through the series combination. Remove the key from the plug to avoid unnecessary heating of wires. How does it happen? Think it in accordance with the Joule’s law of heating.)
- Repeat the activity for three different values of current through the circuit and record the readings of the ammeter and voltmeter in each case. The current through the circuit may either be decreased or increased by changing the number of cells in the circuit (or by changing the settings of the battery eliminator terminal).
Observations and Calculations
(i) Range of the ammeter = ____ - ____ A.
(ii) Least count of the ammeter = ____ A.
(iii) Range of the voltmeter = ____ - ____ V.
(iv) Least count of the voltmeter = ____ V.
(v) Resistance of first resistor R1 = ____ Ω.
(vi) Resistance of second resistor, R2 = ____Ω

R1 = _____ Ω, R2 = _____ Ω
Equivalent resistance [from Eq. (1)] = R1 R2 /(R1 + R2)
= ___ Ω
Results and Discussion
Compare the observed value of the equivalent resistance of the parallel combination of the two given resistors (from the observation table) with the calculated value using Eq. (1).
Precautions and sources of error
- The connecting wires should be thick copper wires, and the insulation of their ends should be removed using sandpaper.
- Connections should be tight; otherwise, some contact resistance may be introduced in the circuit.
- The ammeter should be connected in series with the combinations of resistors such that the current enters at the positive terminal and leaves at the negative terminal of the ammeter.
- The voltmeter should always be connected in parallel to the combinations of resistors.
- The pointers of the ammeter and voltmeter should be at the zero mark when no current passes through the circuit. If not, then ask your teacher to correct it.
- Current should be passed through the circuit for a short time while taking observations; otherwise, current would cause unnecessary heating in the circuit. Heating may change the resistance of resistors.
Note for the Teacher
- The internal resistance of cells should be much lower than the resistance of external resistors used in the experiment.
- In case an accumulator or battery is used in place of cells or an eliminator to draw the current in the circuit, then a rheostat or variable resistance box can be used to change the current flowing through the circuit.
- In case your school laboratory possesses the voltmeter and ammeter of ranges other than the prescribed ranges, then the resistors may be chosen such that an appreciable deflection may appear in the ammeter and voltmeter.
Questions
- If two resistors having resistances of 3Ω and 6Ω, respectively, are connected in parallel, what will be the net resistance in the circuit?
- Two resistors having resistances of 4Ω and 6Ω, respectively, are connected in a circuit. It was found that the total resistance in the circuit is less than 4Ω. In what way would the resistances have been connected?
- Two resistors are connected in series and then in parallel. What effect will it have on the readings of the voltmeter and ammeter?
- In what way household appliances should be connected?