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

To find the terminal voltage of the battery, we need to consider the internal resistance of the battery and the external resistance in the circuit. The formula for terminal voltage, V_t, is given by:

V_t = ε - I * r

where:

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

Given:

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

First, calculate the current, I, using Ohm's Law:

I = ε / (R + r)

Substitute the values:

I = 10 / (4 + 1)

I = 10 / 5

I = 2 A

Now, calculate the terminal voltage:

V_t = ε - I * r

V_t = 10 - 2 * 1

V_t = 10 - 2

V_t = 8 V

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

Answer 2

Calculating Terminal Voltage 

Step 1: Use the Formula for Terminal Voltage

The terminal voltage (\(V\)) of a battery is given by:

V = E − I × r

Where \(E = 10V\) is the emf, \(r = 1\Omega\) is the internal resistance, and \(I\) is the current.

Step 2: Calculate the Current

Using Ohm’s law, the total resistance in the circuit is:

R_total = R_ext + r = 4Ω + 1Ω = 5Ω

The current is:

I = E / R_total = 10V / 5Ω = 2A

Step 3: Find the Terminal Voltage

Now, substitute the values to find the terminal voltage:

V = E − I × r = 10V − (2 × 1Ω) = 8V