9) Find the value of unknown resistance X and the current drawn by the circuit from the battery, if no current flows through the galvanometer. Assume the resistance per unit length of the wire AB to be 0.01 Ω/cm.
Answers
Value of Resistance 'x' = 3 Ω
Current drawn by the circuit = 2.8 A
Explanation:
If no current is flowing through the Galvanometer, it means that the given circuit is a BALANCED WHEATSTONE BRIDGE.
In a Balanced Wheatstone Bridge, the ratios of the resistances are equal.
Resistance through 120 cm = 120 × 0.01
= 1.2 Ω
Resistance through 80 cm = 80 × 0.01
= 0.8 Ω
In this case,
\frac{x}{2}
2
x
= \frac{1.2}{0.8}
0.8
1.2
⇒ ∴ x = [1.2 × 2] ÷ 0.8
= 3 Ω ←ANSWER
Effective Resistance = [R₁R₂] ÷ [R₁ + R₂]
= [(3 + 2) × (1.2 + 0.8)] ÷ [3 + 2 + 1.2 + 0.8]
= 10/7 Ω
Potential Difference = 4 V
According to OHM'S LAW,
V = I × R
4 = I × (10/7)
∴ I = {4 × 7) ÷ 10
= 2.8 A ←ANSWER
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