Question

A 4 Ω coil and a 2 Ω coil are connected in parallel. What is their combined resistance? A total current of 3 A passes through the coils. What current passes through the 2 Ω coil?

Answer 1

The coils of the resistors of 4 Ω and 2 Ω are connected in parallel. Therefore:
$$\begin{gathered} \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2} \\ \frac{1}{R}=\frac{1}{4}+\frac{1}{2} \\ \frac{1}{R}=\frac{3}{4} \\ R=\frac{4}{3}\mathrm{\Omega } \end{gathered}$$
Combined resistance of the 4 Ω coil and the 2 Ω coil = 1.33 Ω
Total current = 3 A
The voltage across the whole cicuit,as in case of parallel circuit volatge is same scross all resistances.
V = IR.
V = 3 x 4/3 = 4 V
Therefore, the current through the 2 Ω coil,
I = V/R₁.
I = 4/2 A
I = 2 A