A battery of EMF 10 V, with internal resistance `1 Omega` is being charged by a 120 V d.c. supply using a series resistance of ` 10 Omega`. The terminal voltage of the battery is

Options

A. 20 V
B. 10 V
C. Zero
D. 30 V

Answer

To find the terminal voltage of the battery being charged, we can follow these steps:

### Step 1: Identify the given values
- EMF of the battery (E) = 10 V
- Internal resistance of the battery (r) = 1 Ω
- External resistance (R) = 10 Ω
- Supply voltage (V_s) = 120 V

### Step 2: Calculate the total resistance in the circuit
The total resistance in the circuit is the sum of the internal resistance of the battery and the external resistance:
\[ R_{total} = R + r = 10 \, \Omega + 1 \, \Omega = 11 \, \Omega \]

### Step 3: Calculate the current in the circuit
Using Ohm's law, we can find the current (I) flowing through the circuit. The net voltage across the circuit is the supply voltage minus the EMF of the battery:
\[ I = \frac{V_s - E}{R_{total}} \]
Substituting the values:
\[ I = \frac{120 \, V - 10 \, V}{11 \, \Omega} = \frac{110 \, V}{11 \, \Omega} = 10 \, A \]

### Step 4: Calculate the terminal voltage of the battery
The terminal voltage (V) of the battery when it is being charged can be calculated using the formula:
\[ V = E + I \cdot r \]
Substituting the values:
\[ V = 10 \, V + (10 \, A \cdot 1 \, \Omega) = 10 \, V + 10 \, V = 20 \, V \]

### Conclusion
The terminal voltage of the battery is **20 V**.

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