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Chapter 30: Q. 73 (page 874)

73. II For your final exam in electronics, you're asked to build an LC circuit that oscillates at 10kHz. In addition, the maximum current must be 0.10Aand the maximum energy stored in the capacitor must be 1.0×10−5J. What values of inductance and capacitance must you use?

Short Answer

Expert verified

Part (a) The inductance of the inductor is 2.0mH

Part (b) The capacitance of the capacitor is0.13μF

Step by step solution

01

Step 1. 

The energy stored in the inductor.

E=12LI2

Here, L is the inductance of the inductor and I is the maximum current in the inductor.

E=12LI21.0×10−5J=12L0.10A2L=0.002H1000mH1HL=2.0mH

Hence, the inductance of the inductor is2.0mH

02

Step 2.

The expression of the frequency with which the RC-oscillator oscillates:

f=12πLC

Here, is the capacitance of the capacitor and is the inductance of the inductor. Rearrange the above equation.

C=14π2(f)2LC=14π210kHz1000Hz1kHz22.0×10−3H=0.13×10−6F1μF10−6F=0.13μF

Therefore, the capacitance of the capacitor is0.13μF

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