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 is given by:

$V_{terminal} = E - Ir$

where $E$ is the emf, $I$ is the current, and $r$ is the internal resistance.

Total resistance, $R_\text{total} = 4 \, \Omega + 1 \, \Omega = 5 \, \Omega$.

Current, $I = \frac{E}{R_\text{total}} = \frac{10}{5} = 2 \, A$.

Terminal voltage, $V_{terminal} = 10 - 2 \times 1 = 8 \, V$.

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