A battery of emf 12 V and internal resistance 3 Ω is connected to an external resistor. If the current in the circuit is 0.6 A, the voltage across the external re sistor will be

The correct option is 10.2 V.

To find the voltage across the external resistor (also known as the terminal voltage of the battery), we can analyze the relationship between the electromotive force (emf) of the battery, its internal resistance, the current in the circuit, and the potential difference across the external load.

Let the electromotive force (emf) of the battery be represented by E, where:

$E=12 \mathrm{V}$

Let the internal resistance of the battery be represented by r, where:

$r=3 \mathrm{\Omega }$

Let the current flowing through the circuit be represented by I, where:

$I=0.6 \mathrm{A}$

When a battery supplies current to an external circuit, some voltage is lost internally across its own internal resistance. This internal voltage drop (often called "lost volts") is given by Ohm's law as the product of the current and the internal resistance:

$V_{\mathrm{internal}}=I\times r$

Substituting the given values:
$V_{\mathrm{internal}}=0.6 \mathrm{A}\times 3 \mathrm{\Omega }=1.8 \mathrm{V}$

The terminal voltage (V) across the external resistor is the emf of the battery minus this internal voltage drop:

$V=E-(I\times r)$

Substituting the values into the formula:
$V=12 \mathrm{V}-1.8 \mathrm{V}$
$V=10.2 \mathrm{V}$

Therefore, the voltage across the external resistor is 10.2 V, which corresponds to the first option.