Question

A current of 9A enters point P of an equilateral triangle PQR having three wires of \(3\Omega\) each and leaves by point R. The currents \(I_1\) and \(I_2\) are respectively

• A. \(2A,7A\)
• B. \(3A,6A\)
• C. \(5A,4A\)
• D. \(6A,3A\)

Hint:

At balance, the resistances are in the ratio of the lengths of the wire.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a metre bridge at balance, \(\frac{R_{left}}{R_{right}} = \frac{l}{100 - l}\), where l is the length measured from the left end.

Step 2: Find the balance length:
\[ \frac{15}{45} = \frac{l}{100 - l} \Rightarrow 100 - l = 3l \Rightarrow l = 25\text{ cm} \]

Step 3: Distance from the centre:
The centre of the wire is at 50 cm, so the null point is \(50 - 25 = 25\) cm from the centre. Option (C), 40 cm, would be the balance length for a ratio of 2:3.

Final Answer:
The null point is 25 cm from the centre, option (D). \[ \boxed{25\text{ cm}} \]