Question:

The terminal voltage of the battery, whose emf is10V10V and internal resistance1Ω, when connected through an external resistance of 4Ω as shown in the figure is:
 

Updated On: Apr 5, 2025
  • 4V4 V
  • 6V6 V
  • 8V8 V
  • 10V10 V
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The Correct Option is C

Approach Solution - 1

The terminal voltage is given by:

Vterminal=EIrV_{terminal} = E - Ir

where EE is the emf, II is the current, and rr is the internal resistance.

Total resistance, Rtotal=4Ω+1Ω=5ΩR_\text{total} = 4 \, \Omega + 1 \, \Omega = 5 \, \Omega.

Current, I=ERtotal=105=2AI = \frac{E}{R_\text{total}} = \frac{10}{5} = 2 \, A.

Terminal voltage, Vterminal=102×1=8VV_{terminal} = 10 - 2 \times 1 = 8 \, V.

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Approach Solution -2

Calculating Terminal Voltage 

Step 1: Use the Formula for Terminal Voltage

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

V = E − I × r

Where E=10VE = 10V is the emf, r=1Ωr = 1\Omega is the internal resistance, and II is the current.

Step 2: Calculate the Current

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

Rtotal = Rext + r = 4Ω + 1Ω = 5Ω

The current is:

I = E / Rtotal = 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

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