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Current Electricity question

2005 · Shift 0 · Q141
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Current Electricity question

2005 · Shift 0 · Q141

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
In the circuit, the galvanometer GGG shows zero deflection. If the batteries AAA and BBB have negligible internal resistance, the value of the resistor RRR will be - AIEEE 2005 Physics - Current Electricity Question 333 English
  1. A
    100Ω100\Omega100Ω
  2. B
    200Ω200\Omega200Ω
  3. C
    1000Ω1000\Omega1000Ω
  4. D
    500Ω500\Omega500Ω
View written solutionFree

Correct answer: A

  1. Use the condition for zero deflection of galvanometer

If the galvanometer shows zero deflection, then the two junctions connected by the galvanometer are at the same potential.

That means the circuit is a balanced bridge.

So, for the two arms,

R1R2=R3R4\frac{R_1}{R_2}=\frac{R_3}{R_4}R2​R1​​=R4​R3​​

  1. Apply balance condition to the given circuit

From the figure, the ratio of resistances in one branch is equal to the ratio in the other branch. Using the values shown in the circuit, we get

R200=12\frac{R}{200}=\frac{1}{2}200R​=21​

Therefore,

R=200×12=100 ΩR=200\times \frac{1}{2}=100\,\OmegaR=200×21​=100Ω

  1. Check options
  • A: 100Ω100\Omega100Ω ✅
  • B: 200Ω200\Omega200Ω ❌
  • C: 1000Ω1000\Omega1000Ω ❌
  • D: 500Ω500\Omega500Ω ❌

Hence, the required resistance is

100 Ω\boxed{100\,\Omega}100Ω​

  1. Comparison with stored answer

Stored correct answer: A

Our derived answer: A

So, the derived answer agrees with the stored answer.

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