Two conducting wires of the same material and equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be : (a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1

Question:

Two conducting wires of the same material and equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be :

(a) 1 : 2 (b) 2 : 1

Answer:

Explanation : The wire is made of the same conducting material, having equal length and width, thus each wire has the same resistance = R

For series combination :

R_S = R + R

= 2R

‍

For parallel combination :

1/R_P = 1/R + 1/R

1/R_P = 2/R

R_P = R/2

‍

Electric Power

P = V²t/R

‍

For series combination, the heat released

P_S = V²t/R_S

P_S = V²t/2R

‍

For parallel combination, the heat released :

P_P= V²t/R_P

P_P= V²t/(R/2)

‍

⇒ P_S/P_P = (V²t/2R) / (V²t/(R/2))

P_S/P_P = (V²t/2R) X (R/2)/V²t // Cancelling V²t by V²t

P_S/P_P = 1/2R X R/2 // Cancelling R by R

P_S/P_P = 1/2 x 1/2

P_S/P_P = 1/4

‍

Hence.

P_S : P_P = 1 : 4

Chapter 11

Question:

Answer:

Class 10 Important Questions

NCERT Solutions for Class 10