Question

The terminal voltage of the battery, whose emf is\(10V\) and internal resistance\(1Ω\), when connected through an external resistance of \(4Ω\) as shown in the figure is:
 

• A. \(4 V\)
• B. \(6 V\)
• C. \(8 V\)
• D. \(10 V\)

Answer 1

The Correct Option is C

The terminal voltage of a battery is determined by its internal resistance and the external circuit resistance. The terminal voltage, denoted as V_t, is calculated using the formula:

V_t = ε - I * r

where:

• ε represents the electromotive force (emf) of the battery in volts.
• I is the current flowing through the circuit in amperes.
• r signifies the internal resistance of the battery in ohms.

Given the following values:

• ε = 10 V
• r = 1 Ω
• External resistance R = 4 Ω

First, determine the circuit current, I, using Ohm's Law:

I = ε / (R + r)

Substituting the provided values:

I = 10 / (4 + 1)

I = 10 / 5

I = 2 A

Next, compute the terminal voltage:

V_t = ε - I * r

V_t = 10 - 2 * 1

V_t = 10 - 2

V_t = 8 V

Therefore, the terminal voltage of the battery is 8 V.