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

In the given circuit, the external resistor (resistance R) and the internal resistance of the cell (resistance r) are connected in series.
The total resistance of the circuit is the sum of the external and internal resistances.
Total Resistance ($R_{total}$) = $R + r$.
The total electromotive force (emf) of the circuit is E.
According to Ohm's Law, the current (I) in a circuit is given by the total voltage (or emf) divided by the total resistance.
$I = \frac{\text{Total EMF}}{\text{Total Resistance}}$.
Substituting the values, we get:
$I = \frac{E}{R+r}$.