For the circuit shown below find the equivalent resistance t

For the circuit shown below, find: the equivalent resistance the power dissipated across the marked 6ohm resistor the total power dissipated by all the resistors

Solution

Here

a) for the equivalent resistance

1/Req = (1/(12 + 6)) + 1/(6 + 1/(1/6 + 1/6))

1/Req = 1/18 + 1/(6 + 3)

1/Req = 1/18 + 1/9

Req = 6 Ohm

the equivalent resistance is 6 Ohm

b)

current through 6 Ohm , I= 12/(12 + 6)

current through 6 Ohm , I= 2/3 A

power dissipated by 6 ohm = (2/3)^2 * 6

power dissipated by 6 ohm = 2.67 W

c)

Total power dissipated = V^2/Req

Total power dissipated = 12^2/6

Total power dissipated = 24 W