Question

An inductor-coil, a capacitor and an AC source of rms voltage 24 V are connected in series. When the frequency of the source is varied, a maximum rms current of 6.0 A is observed. If this inductor coil is connected to a battery of emf 12 V and internal resistance 4.0 Ω, what will be the current?

Answer 1

RMS value of voltage, E_rms = 24 V
Internal resistance of battery, r = 4 Ω
RMS value of current, I_rms = 6 A
Reactance $\left(R\right)$ is given by,
$$\begin{gathered} R=\frac{E}{I_{\mathrm{rms}}} \\ \Rightarrow R=\frac{24}{6}=4\mathrm{\Omega } \end{gathered}$$
Let R' be the total resistance of the circuit. Then,
R' = R + r
$\Rightarrow$ R' = 4 Ω + 4 Ω
$\Rightarrow$R' = 8 Ω

Current, I = $\frac{12}{8}\mathrm{A}$
= 1.5 A