The ratio of heat dissipated per second through the resistance $5\Omega$ and $10\Omega$ in the circuit given below is :

JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Current Electricity

The ratio of heat dissipated per second through the resistance

5Ω

and

10Ω

in the circuit given below is :

Answer: (B)

The

5Ω

and

10Ω

resistors share the same voltage (they are the two parallel branches), so the current divides inversely with resistance:

\frac{i _{1}}{i _{2}} = \frac{10}{5} = 2

, where

i_{1}

flows through the

5Ω

branch.
Power dissipated

P = i^{2} R

, so

\frac{P _{1}}{P _{2}} = (\frac{i _{1}}{i _{2}})^{2} \times \frac{R _{1}}{R _{2}} = (2)^{2} \times \frac{5}{10} = 4 \times \frac{1}{2} = 2

The ratio of heat dissipated is

2 : 1

JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Single correct option