Question

The impedance of $P$ at this frequency is :

• A. $77\Omega$
• B. $36\Omega$
• C. $40\Omega$
• D. $125\Omega$

Answer 1

Answer: (A)

$77\Omega$
has $R_1=32\Omega$ $C_1=1\mu F$
has $R_2=68\Omega$ $L_2=4.8mH$
Total impedance of the series combination of and :
$Z=R_1+R_2+jL\omega -j\frac{1}{C\omega }$
The frequency is adjusted so that maximum current flows in and . that is, frequency is adjusted to have minimum total series impedance. Total series impedance will be minimum when the reactance of L and C cancel each other. Therefore,
$\omega =\frac{1}{\sqrt{LC}}=\frac{100000}{7}rad/s$
Therefore at maximum current, impedance of = $R_1+-j\frac{1}{C\omega }=32-70j=77\Omega$