Assignment #22

Section 30-6

Date Due: Mon. Nov. 17

22. An ideal solenoid with 520 turns {350 turns} is 15.0 cm long and has a radius of 3.80 cm. The wire in the loops of the solenoid carries an initial current of 11.0 Amps. When the circuit is switched off the current decays exponentially according to I(t) = I_o e^-t/t where I_o = 11.0 A and t = 4.70 ms.

(A) What is the size of the magnetic field anywhere inside the solenoid initially? What is the size of the magnetic field anywhere outside the solenoid initially? Ans:{32.3 mT, ?}

(B) 8.50 ms after the circuit is switched off , what is the total magnetic flux F_B through all the loops of the solenoid? 8.50 ms after the circuit is switched off, what is the rate at which the total flux F_B is changing? Ans:{8.39 mT^.m², -1.79 T^.m²/s}

(C) What is the self-inductance L for this solenoid 8.50 ms after the circuit is switched off? Does L change with time? Ans:{4.66 mH,?}

(D) What is the size of the induced emf across the solenoid 8.50 ms after the circuit is switched off? Which direction is the induced emf across the solenoid? Ans:{1.79 V,?}

BONUS:

(E) What is the size of the self induced emf across the coil of the solenoid just before the circuit is switched off? What is size of the self induced emf across the coil of the solenoid the moment the circuit is switched off? Ans:{?, 10.9 V}

Assignment #23

Section 30-7 & 30-8

Date Due: Tue. Nov. 18

23. For the circuit shown the emf is 24.0 V {45.0 V}, the inductor L = 35.0 mH {71.0 mH}, R₁ = 62.0 W, and R₂ = 31.0 W.

(A) What are the time constants of this circuit when the switch is closed and later when the switch is opened? Ans:{t₁ = 1.15 ms, t₂ = 763 ms}

(B) 720 ms after the switch is closed, what is the voltage drop across the resistor R₁ and the energy stored in the inductor? Ans:{21.0 V, 4.07 mJ}

(C) After the current in the circuit reaches its maximum value, the switch is opened. How long will it take (after the switch is opened) for the voltage drop across resistor R₂ to be equal to 3.00 volts? Ans:{1.54 ms}

(D After the switch is first closed the switch is opened at 880 ms {2.40 ms}, this is before the current has reached its maximum value . How long will it take (after the switch is opened) until the induced emf of the coil is equal to 11.0 V? Ans:{1.28 ms}

BONUS:

(E) The switch is opened after the current in the circuit reaches its maximum value. Show that the energy dissipated through the two resistors (in joules) in a time t (after the switch is opened) is given by

Assignment #24

Section 31-2 & 31-3

Date Due: Wed. Nov. 19

An oscillator is used in a laboratory experiment provides a sinusoidal varying emf source with a maximum voltage of 39.0 volts {15.0 V}, . The oscillator's frequency w can be controlled during the experiment. A three-way switch allows the experimenter to separately switch the different components (either the resistor R, the capacitor C, or the inductor L) into a series circuit with the oscillator.

24-1. The oscillator is connected across a 820 W resistor R.

(A) If the frequency is set to 150 Hz {120 Hz}, determine the current through the resistor at t = 11.0 ms. How many times since t = 0 (including the current value) has the current through the resistor been equal to the current at 11.0 ms? Ans:{16.6 mA, 4 times}

(B) Determine the frequency needed to produce +12.0 V across the resistor at t = 31.0 ms under the conditions that this is the first time (since t = 0) the voltage is both +12.0 V across the resistor and also decreasing {increasing}. Ans:{4.76 kHz}

24-2. When the oscillator is connected across a 26.0 nF {81.0 pF} capacitor C, and the frequency of the oscillator is set to 6.70 MHz,

(A) determine the maximum charge acquired by the capacitor and the maximum current flow through the circuit. If the frequency of the oscillator is lowered, what will happen to the magnitude of the value of the maximum charge acquired by the capacitor and the maximum current flow through the circuit. Ans:{1.22 nC, 51.1 mA,?}

(B) Determine the current through the circuit at t = 5.90 ms. Ans:{-50.2 mA}

24-3. The oscillator is switched across a 73.0 mH {45.0 mH} inductor.

(A) When the maximum current flow through the circuit is 6.60 mA, determine inductive reactance of the inductor and the oscillator's frequency. Ans:{2.27 kW, 8.04 kHz}

(B) Determine the current through the circuit when t = 23.0 ms. Ans:{-2.63 mA}

Assignment #25

Section 31-4 & 31-6

Date Due: Fri. Nov. 21

25. A series RLC circuit has a resistor R = 87.0 W {5.80 kW}, an inductor L =270 mH, and unknown capacitor C =? When a 48.0 Hz {1.20 kHz} sinusoidal emf source is applied to the circuit, the impedance of circuit is 110 W {6.40 kW}, and the maximum current is 730 mA {5.90 mA}.

(A) What is the maximum voltage of the emf source and the maximum voltage drop across the resistor? Ans:{ 37.8 V, 34.2 V}

(B&C) Assuming that X_L < X_C , Determine the inductive reactance X_L, the capacitive reactance X_C , the capacitance C, and the phase angle f by which the applied potential lags the current? Ans:{2.04 kW, 4.74 kW, 28.0 nF, -25.0^o}

(D) At the moment the current in the circuit reaches half its maximum value, what is the voltage drop across the resistor, the inductor, and the capacitor? Ans:{17.1 V, 10.4 V, -24.2V}

(E) Determine the voltage of the sinusoidal emf source at t = 9.10 ms {350 ms}. Ans:{30.5 V}

Assignment #26

Section 31-6

Date Due: Mon. Nov. 24

26. A series RLC circuit consist of a 68.0 W {38.0 kW} resistor, a 16.0 mH {400 mH} inductor, and a 77.0 nF {50.0 pF} capacitor. The series combination is driven by a variable frequency emf source that delivers rms voltage of 120 V.

(A) When the frequency is set to 250 kHz, what is the peak and rms current through the circuit? Ans:{ I_rms = 195 mA, I_max = 275 mA}

(B) Determine the rms voltage drop across each of the elements in this circuit when the frequency is set to 250 kHz. Ans:{ V_R = 7.39V, V_L = 122 V, V_C = 2.48 V}

(C) Calculate the power factor and the average power dissipated by the resistor {inductor} in the circuit when the frequency is set to 250 kHz. Ans:{.0616, 0 W}

(D) At what frequency will this circuit resonate? What is the average power dissipated across the resistor {capacitor} at this resonance frequency? Ans:{35.6 kHz, 0 W}

(E) At the resonance frequency what is the maximum amount of energy that will be stored in the capacitor and the inductor? Prove your answers mathematically. Ans:{3.99 mJ, 3.99 mJ}