Question

A battery of emf 10 volts and internal resistance 3 \(\Omega\) is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor?

• A. 7 \(\Omega\)
• B. 20 \(\Omega\)
• C. 17 \(\Omega\)
• D. 14 \(\Omega\)

Hint:

Treat the internal resistance as just another resistor in series with the external circuit. The total resistance is simply the sum of both.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
A simple DC circuit consists of a real battery (ideal voltage source in series with an internal resistance) connected to an external load resistor. We are given the emf, internal resistance, and the current, and we need to find the external resistance.


Step 2: Key Formula or Approach:
Ohm's Law applied to the entire circuit: \[ I = \frac{E}{R + r} \] where \(I\) is current, \(E\) is emf, \(R\) is external resistance, and \(r\) is internal resistance.


Step 3: Detailed Explanation:
Given parameters: Emf (\(E\)) = 10 V Internal resistance (\(r\)) = 3 \(\Omega\) Current (\(I\)) = 0.5 A
Substitute these values into the formula: \[ 0.5 = \frac{10}{R + 3} \] Rearranging the formula to solve for \(R + 3\): \[ R + 3 = \frac{10}{0.5} \] \[ R + 3 = 20 \] Subtract 3 from both sides: \[ R = 20 - 3 \] \[ R = 17 \, \Omega \]

Step 4: Final Answer:
The resistance of the resistor is 17 \(\Omega\).