Question

The resistor of resistance \(R\) is connected between the terminals of a cell of emf \(E\) and internal resistance \(r\). The current \(I\) through the circuit is

• A. \(\frac{E}{r}\)
• B. \(\frac{E}{R + r}\)
• C. \(\frac{R + r}{E}\)
• D. \(\frac{E}{R + r}\)

Hint:

For current calculation in a circuit, use Ohm’s law: \(I = \frac{E}{R_{\text{total}}}\), where \(R_{\text{total}}\) is the sum of the resistances.

Answer 1

The Correct Option is B

Step 1: Applying Ohm's Law.
Ohm’s law states that the current \(I\) is given by the total emf divided by the total resistance in the circuit: \[ I = \frac{E}{R_{\text{total}}}. \]

Step 2: Total resistance in the circuit.
The total resistance in the circuit is the sum of the resistance \(R\) and the internal resistance \(r\). Therefore, the total resistance is: \[ R_{\text{total}} = R + r. \]

Step 3: Finding the current.
Now, using Ohm’s law: \[ I = \frac{E}{R + r}. \]

Final Answer: \(\frac{E}{R + r}\).