JEE Main 2024 — Current Electricity Question with Solution

To determine the ratio of heat dissipated per second through resistances $5\Omega$ and $10\Omega$ in the given parallel circuit, let's break it down step by step.

Understanding the Problem

When resistors are connected in parallel:

1. The voltage across each resistor is the same.


2. The power dissipated in each resistor can be found using the formula:

$P=\frac{V^2}{R}$

Applying the Power Formula in Parallel Resistors

Given:

• $R_1=5\Omega$


• $R_2=10\Omega$

Let $V$ be the voltage across the resistors.

Power Dissipated in Each Resistor

For the $5\Omega$ resistor:

$P_5=\frac{V^2}{5}$

For the $10\Omega$ resistor:

$P_{10}=\frac{V^2}{10}$

Finding the Ratio of Powers

Now, let's find the ratio of the power dissipated through the $5\Omega$ resistor to the power dissipated through the $10\Omega$ resistor:

$\frac{P_5}{P_{10}}=\frac{\frac{V^2}{5}}{\frac{V^2}{10}}=\frac{10}{5}=2$

So, the ratio of power dissipated through the $5\Omega$ resistor to the $10\Omega$ resistor is $2:1$.