Question

The resistors $R_1 = 3\Omega$ and $R_2 = 1\Omega$ are connected in parallel to a 20 V battery. Find the heat developed in the resistor $R_1$ in one minute.

• A. 600 J
• B. 800 J
• C. 6000 J
• D. 8000 J
• E. 7000 J

Hint:

For parallel circuits, use $H = \frac{V^2}{R}t$ because $V$ is constant. For series circuits, use $H = I^2Rt$ because $I$ is constant.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In a parallel circuit, the potential difference (voltage) across each resistor is the same and equal to the supply voltage.
Step 2: Key Formula or Approach:
Heat produced ($H$) in a resistor is given by: \[ H = \frac{V^2}{R} \times t \] where $V$ is voltage, $R$ is resistance, and $t$ is time in seconds.
Step 3: Detailed Explanation:
Given: $V = 20 \text{ V}$, $R_1 = 3 \Omega$, and $t = 1 \text{ minute} = 60 \text{ s}$.
The heat developed in $R_1$ is: \[ H = \frac{20^2}{3} \times 60 \] \[ H = \frac{400}{3} \times 60 \] \[ H = 400 \times 20 \] \[ H = 8000 \text{ J} \] Step 4: Final Answer:
The heat developed is 8000 J.