Question 222: Current Electricity

Question

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

Accepted Answer

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:
The voltage across each resistor is the same.
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 $.

Answer

4 : 1

Answer

2 : 1

Answer

1 : 2

Answer

1 : 1

Current Electricity

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

Choose the correct answer: