Question

For the circuit shown in the diagram given below:

Calculate:

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

Answer 1

Given: R₁ = 5 Ω

R₂ = 10 Ω

R₃ = 30 Ω

V = 6 V

i. I₁ = `V/R_1`

I₁ = `6/5`

I₁ = 1.2 A

I₂ = `V/R_2`

I₂ = `6/10`

I₂ = 0.6 A

I₃ = `V/R_3`

I₃ = `6/30`

I₃ = 0.2 A

ii. Total current (I) = I₁ + I₂ + I₃

I = 1.2 + 0.6 + 0.2

I = 2.0 A

iii. `1/R_p = 1/R_1 + 1/R_2 + 1/R_3`

`1/R_p = 1/5 + 1/10 + 1/30`

`1/R_p = (6 + 3 + 1)/30`

`1/R_p = 10/30`

`1/R_p = 1/3`

R_p = 3 Q