Question

A supply of 24V is applied across a resistance combination consisting of the following: three resistors of 6Ω, 12Ω, and 36Ω connected in parallel and a fourth resistor of 16.4 Ω connected in series with the parallel group. Find the total circuit current.

a) 1.2 A
b) 2.4 A
c) 3.6 A
d) 4.8 A

Answer 1

The total circuit current is 1.2 A.

Step-by-step explanation:

To find the total circuit current, we need to calculate the current flowing through the resistors in the circuit.

First, let's calculate the current flowing through the parallel combination of resistors (6Ω, 12Ω, and 36Ω).

We can use Ohm's Law (I = V/R) to find the current through each resistor:

I₁ = 24V / 6Ω = 4A

I₂ = 24V / 12Ω = 2A

I₃ = 24V / 36Ω = 0.67A

Next, we can find the total resistance of the parallel combination:

1/Rp = 1/6Ω + 1/12Ω + 1/36Ω = 0.5Ω

Rp = 1 / (0.5Ω) = 2Ω

Now, we can find the total circuit current by using Ohm's Law again:

I = V / R = 24V / (2Ω + 16.4Ω) = 1.2A