Question

If two conducting wires of the same length and cross section are combined first in a series and then in a parallel combination, what would be the ratio between the quantity of heat generated in the two series and parallel circuits?
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Answer 1

Answer:

Two conducting wires of the same material and of equal lengths and equal diameter 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 2

Answer:

Let resistance of each wire is R Ω.  if two wires are connected in series, then its equivalent resistance is,  

           =>        R + R = 2R Ω .

If two wires are connected in parallel, then its equivalent resistance is,

           =>        1/R + 1/R  = (1+1)/R = 2/R Ω .

           =>             resistance = R/2

Let Current drawn by series combination = V/2R  = i A.

Current drawn by parallel combination = V / (R/2)  = 4i A

Heat produced in series combination = i2 2R = (2i2 R) W   --- (1)

Heat produced in parallel combination = 16i2 (R/2)  = ( 8i2 R) W ---(2)

From eqn.(1) and (2), we get ratio of heat produced in series combination to heat produced in parallel combination = 1 : 4

Explanation: