Two conductors have the same resistances at 0 ° C but their temperature coefficients of resistance are α 1 and α 2 . The respective temperature coefficients for their series and parallel combinations are :

Step-by-step solution

Change in resistance due to temperature is given by, R ' = R 1 + α ∆ T For Series Combination: R e q = R 1 + R 2 ⇒ 2 R 1 + α e q ∆ T = R 1 + α 1 ∆ T + R 1 + α 2 ∆ T ⇒ 2 R 1 + α e q ∆ T = 2 R + α 1 + α 2 R ∆ T ⇒ α e q = α 1 + α 2 2 For Parallel Combination: 1 R e q = 1 R 1 + 1 R 2 ⇒ 1 R 2 1 + α e q ∆ T = 1 R 1 + α 1 ∆ T + 1 R 1 + α 2 ∆ T ⇒ 2 1 + α e q ∆ T = 1 1 + α 1 ∆ T + 1 1 + α 2 ∆ T ⇒ 2 1 + α e q ∆ T = 1 + α 2 ∆ T + 1 + α 1 ∆ T 1 + α 1 ∆ T 1 + α 2 ∆ T ⇒ 2 1 + α 1 ∆ T 1 + α 2 ∆ T = 2 + α 1 + α 2 ∆ T 1 + α e q ∆ T