(c) 1 : 4

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

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For parallel combination :

1/R_P = 1/R + 1/R

1/R_P = 2/R

R_P = R/2

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Electric Power

P = V²t/R

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For series combination, the heat released

P_S = V²t/R_S

P_S = V²t/2R

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For parallel combination, the heat released :

P_P =  V²t/R_P

P_P = V²t/(R/2)

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⇒ 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

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Hence.

P_S : P_P = 1 : 4