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Transcript
1. A 12.6 V battery is in a circuit with a 30 mH inductor and a 0.150 Ω resistor, as in
Figure 1. The switch is closed at t=0. (a) Find the time constant of the circuit. (b)
Find the current after one time constant has elapsed. (c) Calculate the energy in
the inductor after one time constant has elapsed. (d) Find the voltage drops across
the resistance when t= 0 and t= one time constant. (e) What’s the rate of change
of the current after one time constant?
Figure 1
2. A 6.0 V battery is connected in series with a resistor and an inductor. The
series circuit has a time constant of 600 μs, and the maximum current is 300 mA.
What’s the value of the inductance?
3. Calculate the resistance in an RL circuit in which L = 2.50 H and the current
increases to 90.0% of its final value in 3.00 s.
4. How much energy is stored in a 70 mH inductor at an instant when the current is
2.00 A?
5. A 24 V battery is connected in series with a resistor and an inductor, with R= 8.0 Ω
and L= 4.0 H, respectively. Find the energy stored in the inductor (a) when
the current reaches its maximum value and (b) one time constant after the switch
is closed.
6. An AC voltage source has an output of Δv= (2.00×102 V) sin 2πft. This source
is connected to a 1.00×102 Ω resistor as in Figure 2. Find the rms voltage
and rms current in the resistor.
Figure 2
7. An 8.00 μF capacitor is connected to the terminals of a 60.0 Hz AC source whose
rms voltage is 150 V. Find the capacitive reactance and the rms current in
the circuit.
8. In a purely inductive AC circuit (see Fig. 3), L= 25.0 mH and the rms voltage is 150
V. Find the inductive reactance and rms current in the circuit if the frequency is
60.0 Hz.
Figure 3
9. A series RLC AC circuit has resistance R= 250 Ω, inductance L=0.600 H, capacitance
C= 3.50 μF, frequency f= 60.0 Hz, and maximum voltage Δvmax= 150 V. Find (a) the
impedance, (b) the maximum current in the circuit, (c) the phase angle, and (d)
the maximum voltage across the elements.
10. Calculate the average power delivered to the series RLC circuit in Ex 9.
11. Consider a series RLC circuit for which R = 150 Ω, L = 20.0 mH, ΔVrms = 20.0 V,
and f= 796 s-1. (a) Determine the value of the capacitance for which the
rms current is a maximum. (b) Find the maximum rms current in the circuit.
Answers
1. (a)0.200 s (b) 53.1 A (c) 42.3 J (d) 0 V; 7.97 V (e) 150A/s
2. 12mH
3. 1.92 Ω
4. 0.140 J
5. (a) 18 J (b) 7.2 J
6. (a) 141 V (b) 1.41 A
7. (a) 332 Ω (b) 0.452 A
8. (a) 9.42 Ω (b) 15.9 A
9. (a) 588 Ω (b) 0.255 A (c) -64.8o (d) 63.8V; 57.6V; 193V
10. 8.12 W
11.(a) 2.00×10-6 F (b) 0.133 A