Physics 123 Exam #4 Fall 2002
Do any THREE of the following four questions. X-OUT the question you OMIT.

1. A 66.0 mH inductor with an internal resistance of 270 Ω is placed in parallel with a 1.50 kΩ resistor. The combination is connected to 9.60 V DC battery.

(A) What is the time constant of the inductor branch of the circuit?
Ans:{244 ms}

(B) After the switch is closed, how long will it take for the current in the inductor branch of the circuit to equal 11.0 mA?
Ans:{90.5 ms}

(C) If the switch is open 380 ms after it is first closed, how many joules of energy will be dissipated as the current decays by both the 1.50 k W resistor and the inductor’s internal resistance 270 W?
Ans:{26.0 mJ}
2. An A.C. circuit consist of a sinusoidal current source I = Imax sin(ω t) with a maximum voltage of 15.0 V. The emf source is also in series with two capacitors (C1 = 2.40 mF and C2 = 1.30 mF) and a 2.80 mH inductor. The frequency of the emf source is 8.20 kHz.
(A) What is the total impedance of the circuit?
Ans:{121 W}

(B) What is the voltage across the inductor when t = 150 ms?
Ans:{2.24 V}

(C) What is the maximum charge on either capacitor?
Ans:{2.40 mC}
3. A RLC circuit has a resistor R = 33.0 Ω, an unknown inductor L, and a capacitor C = 5.80 mF. A sinusoidal current source I = Imax sin(ω t) produces a maximum current of 41.0 mA. When the circuit is driven at a frequency of 900 Hz, the voltage leads the current by 30.0o.
(A) What is the inductance of L?
Ans:{8.76 mH}

(B) What is the rms voltage across the capacitor?.
Ans:{884 mV}

(C) What is the voltage of the emf current source at the start when t = 0? (It is not zero.)
Ans:{781 mV}
4. When 1.40 kΩ resistor and a 670 mH inductor are connected in series to sinusoidal current with a maximum current of 1.80 A. The impedance of the circuit is 4.30 kΩ.
(A) What is the angular frequency of this AC circuit? (Hint: find the impedance of the inductor first.)
Ans:{6070 rad/s}

(B) What is the phase angle of the voltage across the inductor and the resistor?
Ans:{1.24 rad}

(C) What is the average power dissipated by this circuit?
Ans:{2.27 kW}

Physics 123 Exam #4 Spring 2002

1.A ideal solenoid with 370 turns has cross-sectional area of 33.0 cm2 and a length of 18.0 cm. The solenoid is placed in a circuit with a 560 Ω resistor and a 110 volt DC battery.

(A) What is the time constant of this circuit?
Ans:{5.63 ms}

(B) What is the maximum energy that this solenoid can store in this circuit?
Ans:{60.8 mJ}

(C) What is the size of the magnetic field inside the solenoid 2.20 ms after the circuit is closed?
Ans:{164 mT}
2. A circuit consist of 45.0 volt DC battery in parallel with a 42 Ω resistor and a 78.0 mH inductor that is in series with an 39.0 kΩ resistor as shown.
(A) After the switch is closed what is the maximum current through the inductor?
Ans:{1.15 mA}

(B) What is the energy stored in the inductor 1.00 ms after the switch is closed?
Ans:{8.04 nJ}

(C) How long will it take for the voltage drop across the inductor to equal 26.0 volts?
Ans:{1.10 ms}
3. A RLC series circuit has resistance R = 245Ω, an inductance L = 1.90 mH, and a capacitance C = 21.0 nF. A sinusoidal current I = Imax sin(ω t) that has a maximum current of 7.50 mA every 45.0 µs.
(A) What is impedance of this circuit ?
Ans:{256 W}

(B) What is voltage across the capacitor every time the current is equal to zero?
Ans:{-2.56 V}

(C) Does the voltage lag or lead the current across the RLC circuit and by how many microseconds?
Ans:{-2.15 ms, Voltage Lags}
4. A RLC series circuit has resistance of 44.0 Ω, an inductive reactance of 57.0 Ω, and capacitive reactance of 39.0 Ω. The series combination is driven by rms voltage of 90.0 V source.
(A) What is the maximum value of the current in this circuit if the oscillator is driven at a frequency of 18.0 kHz?
Ans:{2.68 A}

(B) What is the rms voltage drop across the capacitor if the oscillator is driven at a frequency of 18.0 kHz?
Ans:{73.8 V}

(C) At what frequency (in Hz) must this circuit be driven so that it will dissipate the maximum amount of heat energy in the resistor ? Ans:{14.9 kHz}