#### Question

In the circuit diagram given below, three resistors R1, R2, and R3 of 5 Ω, 10 Ω and 30 Ω, respectively are connected as shown

Calculate:

(a) current through each resistor.

(b) total current in the circuit.

(c) total resistance in the circuit.

#### Solution

(a) Let *I*_{1}, *I*_{2} and *I*_{3} be the current flowing through the resistors of 5 Ω, 100 Ω and 30 Ω, respectively.

According to Ohm's law, *V* = *IR*

Here, *V* = 12 V and *R* = 5 Ω*I *= *V*/*R**I*_{1} = 12/5 = 2.4 A*I*_{2} = 12/10 = 1.2 A*I*_{3} = 12/30 = 0.4 A

(b) Total current through the circuit, *I* = *I*_{1} + *I*_{2} + *I*_{3}

= 2.4 A + 1.2 A + 0.4 A

= 4 A

(c) The resistors of 5 Ω, 100 Ω and 30 Ω are connected in parallel. Therefore, the net resistance will be:

1/ *R* = 1/*R*_{1} + 1/*R*_{2} + 1/*R*_{3}

1/*R* = (1/5) + (1/10) + (1/30)

1/*R* = (6 + 3 +1)/30

I/*R* = 10/30*R* = 3 Ω