Question

The internal resistance of a cell of e.m.f. 2 V is $0.1\, \Omega$ It is connected to a resistance of $3.9\, \Omega$. The voltage across the cell will be

• A. 1.95 V
• B. 1.9 V
• C. 0.5 V
• D. 2 V

Answer 1

The Correct Option is A

To find the voltage across the cell, we can use the concept of internal resistance in a cell when a load is connected. The formula to calculate the terminal voltage (V) across the cell is given by:

V = \text{E.M.F} - I \cdot r

where:

• \text{E.M.F} is the electromotive force of the cell (2 V in this case).
• I is the current through the circuit.
• r is the internal resistance of the cell (0.1\, \Omega).

First, we need to calculate the current (I) in the circuit using Ohm's law:

I = \frac{\text{E.M.F}}{R + r}

where R is the external resistance (3.9\, \Omega).

Substituting the values:

I = \frac{2}{3.9 + 0.1} = \frac{2}{4} = 0.5 \, \text{A}

Now, using the formula for terminal voltage:

V = 2 - 0.5 \times 0.1 = 2 - 0.05 = 1.95 \, \text{V}

Therefore, the voltage across the cell is 1.95 V.

This matches the given option: 1.95 V.