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

To find the resistance of the resistor, we can use Ohm's Law and the total circuit resistance equation. The total voltage across the circuit is the emf provided by the battery, and we have:

• Battery emf (E): \(10 \, \text{V}\)
• Internal resistance of the battery (r): \(3 \, \Omega\)
• Current in the circuit (I): \(0.5 \, \text{A}\)

The formula for the total voltage across a circuit is given by:

\(V = I \times R_{\text{total}}\)

Where \(R_{\text{total}}\) is the total resistance in the circuit, which is the sum of the internal resistance of the battery and the resistance of the external resistor (R). Thus, we can express:

\(R_{\text{total}} = R + r\)

Substituting the known values into the voltage equation:

\(10 = 0.5 \times (R + 3)\)

Solving for \(R\):

1. First, divide both sides by the current to express in terms of resistance:
2. Then, subtract the internal resistance from both sides:

Therefore, the resistance of the resistor is 17 Ω. Thus, the correct answer is 17 Ω.