Current in a circuit

Question

Answer 1

(1)

Step 1:

Redraw the circuit showing branch currents.

Apply KVL for the first loop.

Apply KVL for the second loop.

Substitute in equation (1).

Since the current is in opposite direction to the assumed current direction, .

Solution :

The current flowing in the second loop is .

Answer 2

(2)

Step 1:

Observe the circuit.

Apply KVL for the first loop.

The loop current is .       (From (1))

The current in the first loop is .

Solution :

The current in the first loop is .

Answer 3

(3)

Step 1:

The loop currents are and .          (From (1) and (2))

The current flowing through the resistor is .

The current flowing through the resistor  is .

Solution :

The current flowing through the resistor  is .