Question

A battery of emf 8 V and internal resistance 4$\Omega$ is connected to an external resistor. The resistance of the external resistor if the current in the circuit is 0.8 A is

• A. 6$\Omega$
• B. 9$\Omega$
• C. 15 $\Omega$
• D. 13 $\Omega$

Answer 1

Answer: (A)

6$\Omega$

Answer 2

The problem involves a battery with an electromotive force (emf) and internal resistance connected to an external resistor. We need to find the value of the external resistance given the current flowing through the circuit.

The formula relating emf ($\mathcal{E}$), internal resistance ($r$), external resistance ($R_{ext}$), and current ($I$) in a simple circuit is given by Ohm's Law for a circuit with internal resistance:

$I = \frac{\mathcal{E}}{R_{ext} + r}$

Given values:

• Emf of the battery, $\mathcal{E} = 8\,V$
• Internal resistance of the battery, $r = 4\,\Omega$
• Current in the circuit, $I = 0.8\,A$

We need to find the external resistance, $R_{ext}$.

Rearrange the formula to solve for $R_{ext}$:

$I(R_{ext} + r) = \mathcal{E}$

$R_{ext} + r = \frac{\mathcal{E}}{I}$

$R_{ext} = \frac{\mathcal{E}}{I} - r$

Now, substitute the given values into the equation:

$R_{ext} = \frac{8\,V}{0.8\,A} - 4\,\Omega$

$R_{ext} = 10\,\Omega - 4\,\Omega$

$R_{ext} = 6\,\Omega$

Thus, the resistance of the external resistor is $6\,\Omega$.