JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Current Electricity

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Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

(A) $4 : 1$ ✓ Correct
(B) $2 : 1$
(C) $1 : 2$
(D) $1 : 4$

Answer: (A)

Solution

At a fixed applied voltage the heat produced in a given time is

H = \frac{V ^{2}}{R} t

, so it varies inversely with resistance. Two equal filaments of resistance

R

give

\frac{R}{2}

in parallel and

2 R

in series. Hence

\frac{H _{p a r a l l e l}}{H _{ser i es}} = \frac{2 R}{R /2} = 4

, a ratio of

4 : 1

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option

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