A cell whose e.m.f. is 2V and internal resistance is `0.1Omega` is connected with a resistance of `3.9Omega` the voltage across the cell terminal will be

Options

A. 0.5 V
B. 1.9 V
C. 1.95 V
D. 72 V

Answer

To find the voltage across the terminals of the cell, we can follow these steps:

### Step 1: Identify the given values
- Electromotive force (e.m.f) of the cell, \( E = 2 \, V \)
- Internal resistance of the cell, \( r = 0.1 \, \Omega \)
- External resistance, \( R = 3.9 \, \Omega \)

### Step 2: Calculate the total resistance in the circuit
The total resistance \( R_{total} \) in the circuit is the sum of the internal resistance of the cell and the external resistance:
\[ R_{total} = R + r = 3.9 \, \Omega + 0.1 \, \Omega = 4.0 \, \Omega \]

### Step 3: Calculate the current flowing through the circuit
Using Ohm's law, the current \( I \) flowing through the circuit can be calculated using the formula:
\[ I = \frac{E}{R_{total}} = \frac{E}{R + r} = \frac{2 \, V}{4.0 \, \Omega} = 0.5 \, A \]

### Step 4: Calculate the potential difference across the external resistance
The potential difference \( V_R \) across the external resistance \( R \) can be calculated using Ohm's law:
\[ V_R = I \times R = 0.5 \, A \times 3.9 \, \Omega = 1.95 \, V \]

### Step 5: Calculate the voltage across the terminals of the cell
The voltage across the terminals of the cell \( V_{terminal} \) is given by:
\[ V_{terminal} = E - I \times r \]
Substituting the values:
\[ V_{terminal} = 2 \, V - (0.5 \, A \times 0.1 \, \Omega) = 2 \, V - 0.05 \, V = 1.95 \, V \]

### Final Answer
The voltage across the cell terminals is \( 1.95 \, V \).

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