This question is incomplete, the complete question is;
An l-c cirucit with a 70 mh inductor and a 0.54 μF capacitor oscillates. The maximum charge on the capacitor is 11.5 μC. What are the oscillation frequency and the maximum current in this circuit
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Options
a) 1.07 kHz, 63.4 mA
b) 4.38 kHz, 101.3 mA
c) 6.74 kHz, 55.7 mA
d) 2.31 kHz, 93.5 mA
e) 0.82 kHz, 59.1 mA
Answer:
the oscillation frequency and the maximum current in this circuit are; 0.82 kHz and 59.1 mA respectively.
so Option e) 0.82 kHz, 59.1 mA is the correct answer
Explanation:
Given that;
inductor L = 70 mH = 70 × 10⁻³ H
Capacitor C = 0.54 μf = 0.54 × 10⁻⁶ f
Qmax on capacitor = 11.5 μf = 11.5 × 10⁻⁶ c
oscillation frequency in L-C circuit;
f = 1/2π√(LC)
we substitute our values;
f = 1/2π√(70 × 10⁻³ × 0.54 × 10⁻⁶ )
f = 0.0818 × 10⁴ Hz
f = 0.082 × 10³ Hz ≈ 0.82 kHz
Maximum circuit in L-C circuit is given by
I_max = Qmax/√(LC)
we substitute
I_max = 11.5 × 10⁻⁶ / √(70 × 10⁻³ × 0.54 × 10⁻⁶ )
= 59.1 × 10³ A ≈ 59.1 mA
Therefore the oscillation frequency and the maximum current in this circuit are; 0.82 kHz and 59.1 mA respectively.
so Option e) 0.82 kHz, 59.1 mA is the correct answer
