Given Electrical Parameters
The problem provides the following values:
- Battery Electromotive Force (emf), $\mathcal{E} = 12 \text{ V}$
- Internal Resistance, $r = 2 \ \Omega$
- Circuit Current, $I = 0.6 \text{ A}$
Formula for Terminal Voltage
The terminal voltage ($V_T$) of a battery is the actual voltage across its terminals when current is flowing. It can be calculated using the formula:
$ V_T = \mathcal{E} - Ir $
Where:
- $V_T$ is the terminal voltage
- $\mathcal{E}$ is the battery emf
- $I$ is the current flowing through the circuit
- $r$ is the internal resistance of the battery
Calculation of Terminal Voltage
Substitute the given values into the formula:
$ V_T = 12 \text{ V} - (0.6 \text{ A} \times 2 \ \Omega) $
First, calculate the voltage drop across the internal resistance:
$ I \times r = 0.6 \text{ A} \times 2 \ \Omega = 1.2 \text{ V} $
Now, subtract this voltage drop from the battery's emf:
$ V_T = 12 \text{ V} - 1.2 \text{ V} $
$ V_T = 10.8 \text{ V} $
Result
The terminal voltage of the battery is $10.8 \text{ V}$.
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