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 $10 kHz$ . In addition, the maximum current must be $0.10 A$ and the maximum energy stored in the capacitor must be $1.0 \times 10^{- 5} J$ . What values of inductance and capacitance must you use?

Short Answer

Expert verified

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

Part (b) The capacitance of the capacitor is $0.13 μ F$

Step by step solution

Step 1.

The energy stored in the inductor.

$E = \frac{1}{2} L I^{2}$

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

$\begin{array}{l} E = \frac{1}{2} L I^{2} \\ 1.0 \times 10^{- 5} J = \frac{1}{2} (L) {(0.10 A)}^{2} \\ L = 0.002 H (\frac{1000 mH}{1 H}) \\ L = 2.0 mH \end{array}$

Hence, the inductance of the inductor is $2.0 mH$

Step 2.

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

$f = \frac{1}{2 π \sqrt{L C}}$

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

$\begin{array}{l} C = \frac{1}{4 π^{2} {(f)}^{2} L} \\ C = \frac{1}{4 π^{2} {(10 kHz (\frac{1000 Hz}{1 kHz}))}^{2} (2.0 \times 10^{- 3} H)} \\ = (0.13 \times 10^{- 6} F) (\frac{1 μ F}{10^{- 6} F}) \\ = 0.13 μ F \end{array}$

Therefore, the capacitance of the capacitor is $0.13 μ F$

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

Short Answer

Step by step solution

Step 1.

Step 2.

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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

Step by step solution

Step 1.

Step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Radiation

Quantum Physics

Further Mechanics and Thermal Physics

Engineering Physics

Famous Physicists

Study anywhere. Anytime. Across all devices.

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