Question

Find the value of the 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 is
0.01cm


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Answer 1

Answer:

• 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,

        $\frac{x}{2}$ = $\frac{1.2}{0.8}$

⇒ ∴ 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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