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Exercise:
An ac circuit contains a resistor and a capacitor in series. The impdedance is ZO and the phase shift is dphO. Determine the circuit's resistance and reactance.

Solution:
The impedance for a series circuit with a resistor and a capacitor is Z sqrtR^ + X_C^ labeleq and the phase shift is given by tanDeltaphi frac-X_CR labeleq The impedance can be written as Z R sqrt+leftfracX_CRright^ R sqrt+lefttanDeltaphiright^ Solving for the resistance yields R RF fracZsqrt+lefttandphright^ labeleqR R approx resultRP Solving refeq for the reactance and using refeqR yields X_C -R tanDeltaphi XF -Z times fractandphsqrt+lefttandphright^ X approx resultXP
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Exercise:
An ac circuit contains a resistor and a capacitor in series. The impdedance is ZO and the phase shift is dphO. Determine the circuit's resistance and reactance.

Solution:
The impedance for a series circuit with a resistor and a capacitor is Z sqrtR^ + X_C^ labeleq and the phase shift is given by tanDeltaphi frac-X_CR labeleq The impedance can be written as Z R sqrt+leftfracX_CRright^ R sqrt+lefttanDeltaphiright^ Solving for the resistance yields R RF fracZsqrt+lefttandphright^ labeleqR R approx resultRP Solving refeq for the reactance and using refeqR yields X_C -R tanDeltaphi XF -Z times fractandphsqrt+lefttandphright^ X approx resultXP
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Branches
Electrodynamics
Tags
ac circuit, impedance, phase shift, reactance
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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