Question

A battery of 6 V and internal resistance \(2\,\Omega\) is connected to a silver voltameter. If the current of \(1.5\,A\) flows through the circuit, the resistance of the voltameter is

• A. \(4\,\Omega\)
• B. \(2\,\Omega\)
• C. \(6\,\Omega\)
• D. \(1\,\Omega\)
• E. \(5\,\Omega\)

Hint:

Always use total resistance \(R + r\) in circuits involving internal resistance.

Answer 1

The Correct Option is B

Concept: For a complete circuit, Ohm’s law is: \[ I = \frac{E}{R + r} \] where:
• \(E\) = emf of battery
• \(R\) = external resistance (voltameter)
• \(r\) = internal resistance

Step 1: Write given values. \[ E = 6\,V, \quad r = 2\,\Omega, \quad I = 1.5\,A \]

Step 2: Substitute into formula. \[ 1.5 = \frac{6}{R + 2} \]

Step 3: Solve step-by-step. \[ R + 2 = \frac{6}{1.5} \] \[ R + 2 = 4 \] \[ R = 4 - 2 = 2\,\Omega \]

Step 4: Interpretation. The resistance of the voltameter is the external resistance \(R\). \[ \boxed{R = 2\,\Omega} \]