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: Wire resistance:
Resistance is proportional to length. The left part of the wire with the 15 ohm resistor must be one third as large as the right part with 45 ohm.

Step 2: Lengths:
Left : right = 1 : 3, so left = 25 cm and right = 75 cm. The null point is 25 cm from the left end and 25 cm away from the centre (D).

Final Answer:
25 cm. \[ \boxed{25\text{ cm}} \]