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:

1. current through each resistor.
2. total current in the circuit. 
3. total resistance in the circuit.

Answer 1

a. Let I₁, I₂ and I₃ be the current flowing through the resistors of 5 Ω, 10 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 = I₁ + I₂ + I₃

=  2.4 A + 1.2 A + 0.4 A

= 4 A

c. The resistors of 5 Ω, 10 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