Determine the frequency so that the current Ii and the voltage Vo in Figure P4.52 are in phase.
Zs = 13,000 + j?3 ?
R = 120?
L = 19mH C = 220 pF
Analysis:
is not a factor in this solution. Only R, L, and C will determine if the voltage across this combination is in phase with the current through it. If the voltage and current are in phase, then, the equivalent impedance must have an "imaginary" or reactive part which is zero!
Notes:
1. To separate the equivalent impedance into real (resistive) and "imaginary" (reactive) components, the denominator had to be "rationalized". This was done by multiplying numerator and denominator by the complex conjugate of the denominator, and multiplying term by term. Remember that j2=-1 , etc.
2. The term with R had a negligible effect on the resonant frequency in this case. If R is sufficiently large, however, it will significantly affect the answer.
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