(5%) Problem 18: Two coils, held in xed positions, have a mutual inductance of M: 0.00 74 H. The current in the rst coil is [(2') = Immkmj, Where IO = 4. 6A, a) = I 3.5 rad/s. Randomized Variables M: 0.0074H I 1024.613 co = 13.5 rad/s 1 2 UtlIL-cx pcrltuxum E a 25% Part (a) Express the magnitude of the induced emf in the second coil, .92, in terms of M and I. A 25% Part (b) Express the magnitude of 82 in terms of M; 10, and a). a 25% Part (c) Express the maximum value of \\E'ZI, 8m, in terms of .M, 10, and a). D a 25% Part (d) Calculate the numerical value of 9mm in V. _ Grade Summary 3m _ I Deductions 0% Potential ][H]% (5%) Problem 19: A 4800-pF capacitor is charged to 95 V and then quickly connected to an inductor with 79-mH inductance. A 33% Part (a) Find the maximum energy, in joules, stored in the magnetic field of the inductor. A 33% Part (b) Find the peak value of the current, in amperes. A 33% Part (c) Find the circuit's oscillation frequency, in hertz. Grade Summary Deductions 0% Potential 100%(5%) Problem 20: A circuit is comprised of an inductor, a capacitor, a battery and a switch. When the switch is in position "a", the battery is in series with the capacitor, but the inductor is excluded. When the switch is in position "b", the capacitor and the inductor are in series, but the battery is excluded. Two voltmeters and an anuneter have been added to the circuit, as shown. E 3 8% Part (a) Initially the switch is moved to position "a" where it remains until the capacitor attains its maximum charge. Enter an expression for the maximum charge on the capacitor. E A 8% Part (1)) Once the capacitor is fully charged, the switch is moved from position "a" to position "b". Let q represent the charge on the capacitor, and let I represent the current measured by the ammeter at any given time aer the switch is moved to position "b". Enter an expression for a Kirchhoff Loop Rule equation for the circuit that now includes both the capacitor and the inductor. E 8 8% Part (c) Current is the derivative of charge with respect to time. Use this information to eliminate current from your Kirchhoff Loop Rule equation. Enter an expression for the second derivative of charge with respect to time. E 3 8% Part (d) When the second derivative of a function is proportional to the opposite of the original function, then we know from calculus and from simple harmonic motion that the solution may be represented with a sine or a cosine function. If we write the solution as q(t) : A (306(wt + 9b), consider the initial conditions at the instant the switch is moved to position "b", and enter an expression for the phase constant, :35. E 3 8% Part (e) If we write the solution as q(t) = Acos(wt + qb), consider the initial conditions at the instant the switch is moved to position "b", and enter an expression for the amplitude, A. m 4 8% Part (e) If we write the solution as q(t) = A cos(wt + ), consider the initial conditions at the instant the switch is moved to position "b", and enter an expression for the amplitude, A. A 8% Part (f) Take appropriate derivatives of q(t) = A cos(wt + $) and substitute them into the equation that you previously entered for d2 q in order to dt2 discover an expression for w. Enter that expression. 4 8% Part (g) Enter an expression for the voltage across the capacitor as a function of time as measured by the voltmeter labeled Vc. 4 8% Part (h) Enter an expression for the voltage across the inductor as a function of time as measured by the voltmeter labeled VL. A 8% Part (i) Enter an expression for the sum of the voltages across the inductor and the capacitor. A 8% Part (j) Enter an expression for the energy stored by the capacitor as a function of time. A 8% Part (k) Enter an expression for the energy stored by the inductor as a function of time. A 8% Part (1) Enter an expression for the sum of the energies stored by the capacitor and the inductor as a function of time. A 8% Part (m) Which statement best describes the energy flow in the circuit while the switch is in position "b"? Energy stored in an electric field is used to recharge the battery. Grade Summary Deductions 0% O Energy stored in an electric field dissipates as heat. Potential 100% O Energy is equally stored in electric and magnetic fields at all times. O Energy oscillates back and forth between storage in electric and magnetic fields. Submissions O Attempts remaining: 6 Energy stored in a magnetic field is used to recharge the battery. (0% per attempt) O Energy stored in a magnetic field dissipates to thermal energy. detailed view Submit Hint Feedback I give up!(5%) Problem 21: In the RLC circuit shown on the right R = 0.075 Q, L = 1.6 H, and C = 1.3 F. The initial charge carried by the capacitor is QO 2 0.075 C. The switch is closed at time t = O. C :Utllccxpcrttzwnm E 3 17%: Part (:1) Express Hie angular frequency, a), of damped oscillation in the circuit in terms ofR, L, and C. E 3 17% Part (b) Calculate the angular frequency, a), in radians per second. E 3 17% Part (c) Express the charge, Q, on the capacitor as a function of time in terms of Q0, R, L, and a). E 3 17% Part (d) Calculate the value of Q, in coulombs, at time I: 1 s. E 3 17% Part (e) Express the critical resistance, R5, in terms of L and C. L) 3 17% Part (1') Calculate the value of R0, in ohms. Grade Summary RC 7 I Deductions 0% Potential 100% -,\\| A | .A II I,|\\|...I,.I,.|_____ (5%) Problem 22: An AC current source is connected to an inductor with an inductance _ = 2 H. At time t = 0, the current through the inductor is in = 0 A. The power supply provides a time-dependent current i through the inductor as described by the following equation: i(t) = 10-cos(wt), where c = 500 rad/s. The current is measured in units of Amps. A 33% Part (a) Determine the current through the inductor, in amperes, at time t = 2.5 sec. A 33% Part (b) Determine the voltage across the inductor, in volts, at time t = 2.5 sec. A 33% Part (c) Determine the magnitude of the maximum voltage, in volts, across the inductor. Grade Summary max Deductions 0% Potential 100%