Question

The circuit diagram given below shows the combination of three resistors R₁, R₂ and R₃:


Find :
(i) total resistance of the circuit.
(ii) total current flowing in the circuit.
(iii) the potential difference across R₁.

Answer 1

(i) As shown in the figure, the resistors R₂ and R3 are connected in parallel. Their total resistance is given by:

1/R = 1/R₂+ 1/R₃

Here, R₂ = 3 Ω
R₃ = 6 Ω
So,
1/R = 1/3 + 1/6
Or 1/R = (2+1)/6
1/R = 3/6
R = 2 Ω
This resistance is in series with the resistor, R₁.
Total resistance = 2 Ω + R₁
R₁ = 4 Ω
Therefore, total resistance = 2 Ω + 4 Ω = 6 Ω


(ii) The current through the circuit can be calculated as follows:
Current, I = V / R
I = (12 / 6) A
I = 2 A

(iii) The potential difference across R₁ = 2 A x 4 Ω = 8 V