To determine The value of R , L and C in the circuit Explanation Write the equation for the impedance of the R L C circuit. Z = R 2 + ( X L − X C ) 2 (I) Here, Z is the impedance, R is the resistance, X L is the inductive reactance and X C is the capacitive reactance Write the expression for the peak current in the R L C circuit. I p = V p Z (II) Here, I p is then peak current and V p is the peak voltage At resonance, X L = X C and hence the impedance Z = R Replace Z by R in equation (II) and solve for R . I p = V p R R = V p I p Substitute 15 V for V p and 112 mA for I p to find the resistance R . R = 15 V 112 mA = 15 V 112 mA × 10 − 3 A 1 mA = 134 Ω Substitute 15 V for V p and 44.8 mA for I p in equation (II) to find the impedance of the circuit at the given frequency of 1.22 kHz . 44.8 mA = 15 V Z Z = 20 V 44.8 mA × 10 − 3 A 1 mA × 112 mA 112 mA = ( 112 mA 44.8 mA ) R = 112 44.8 R Write the equation for | X L − X C | form equation (I). | X L − X C | = Z 2 − R 2 (III) Use Z = 112 44.8 R in equation (III). | X L − X C | = ( 112 44.8 R ) 2 − R 2 = R ( 112 44.8 ) 2 − 1 = 1

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Chapter 28, Problem 67P

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