Question

Two identical resistors of resistance Rare connected in series with a battery of potential difference V for time t. The resistors are then connected in parallel with the same battery for the same time t. Compare the heat produced in the two cases.

Answer 1

Given that, two identical resistors of resistance R are connected in series and then in parallel with a battery of potential difference V for time t.

When connected in series combination:

Rs = R + R

Rs = 2R

When connected in parallel combination:

1/Rp = 1/R + 1/R

1/Rp = 2/R

Rp = R/2

Ratio of series and parallel:

Rs/Rp = 2R/(R/2)

Rs/Rp = 4/1

Heat produced when in series combination:

H = I²Rt

(I = V/R and R = 2R)

Hs = (V² × 2Rt)/(2R)²

Hs = V²t/2R

Heat produced when in parallel combination:

H = I²Rt

Hp = V²/(R/2)² × Rt/2

Hp = 4V²/R² × Rt/2

Hp = 2V²t/R

(Hs for heat in series and Hp for heat in parallel)

Ratio of heat produced in series and parallel:

Hs/Hp = (V²t/2R)/(2V²t/R) =1/4

Hs = 1/4 Hp

Therefore, the heat produced in series is 1/4 times of the heat produced in parallel.

Answer 2

Explanation:

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