Answer
Please see the work below.
Work Step by Step
(a) We know that
$f=\frac{1}{2\pi L}[(\frac{V_{rms}}{I_{rms}})^2-R^2]^{\frac{1}{2}}$
We plug in the known values to obtain:
$f=\frac{1}{2\pi\times 31\times 10^{-3}}[(\frac{120}{1.5})^2-(68)^2]^{\frac{1}{2}}$
This simplifies to:
$f=216Hz$
(b) As $V_{rms, R}=I_{rms}\times R$
We plug in the known values to obtain:
$V_{rms, R}=1.5\times 68$
$V_{rms,R}=102V$
(c) We know that
$V_{rms, L}=I_{rms}\times X_L$
$V_{rms,L}=1.5\times 2\pi fL$
We plug in the known values to obtain:
$V_{rms,L}=1.5\times 2\pi\times 216\times 31\times 10^{-3}$
$V_{rms,L}=63V$
(d) As $\sqrt{V^2_{rms,R}+V^2_{rms,L}}=\sqrt{(102)^2+(63)^2}$
$\sqrt{V^2_{rms,R}+V^2_{rms,L}}=\sqrt{10404+3969}=120V$
