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Practice question

MCQ

Question

In a Wheatstone bridge with \( R_1 = 30 \, \Omega \), \( R_2 = 60 \, \Omega \), \( R_3 = 15 \, \Omega
\), and \( R_4 = 32 \, \Omega \), a \( 10 \, \text{V} \) battery is connected across AC. What is the
current through the galvanometer (\( R_g = 10 \, \Omega \))?

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Explanation

**Wheatstone bridge balance** condition R₁/R₂ = R₃/R₄, R₄ = R₂ R₃/R₁, when galvanometer current zero, potentials at midpoints equal. At balance, no current through galvanometer, enabling precise resistance measurement independent of source voltage. Apply Kirchhoff’s rules. Let currents be I₁ (AB), I₂ (AD), I_g (BD). Junction B: I₁ = I_g + I₄ , Junction D: I₂ = I_g + I₃ . Loop BADB: 30 I₁ + 10 I_g - 60 I₂ = 0 ⇒ 3 I₁ + I_g - 6 I₂ = 0 . Loop BCDB: 60 (I₁ - I_g) - 10 I_g - 15 (I₂ + I_g) = 0 ⇒ 4 I₁ - 2

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