A circuit consists of a coil, a switch, and a battery, all in series. The internal resistance of the battery is negligible compared with that of the coil. The switch is originally open. It is thrown closed, and after a time interval Δt, thecurrent in the circuit reaches 80.0% of its final value. The switch then remains closed for a time interval much longer than Δt. The wires connected to the terminals of the battery are then short-circuited with another wire and removed from the battery, so that the current is uninterrupted. (a) At an instant that is a time interval Δt after the short circuit, the current is what percentage of its maximum value? (b) At the moment 2Δt after the coil is short-circuited, the current in the coil is what percentage of its maximum value?

Two circuits contain an emf produced by a moving metal rod, like that shown in the drawing. The speed of the rod is the same in each circuit, but the bulb in circuit 1 has one-half the resistance of the bulb in circuit 2. The circuits are otherwise identical. The resistance of the light bulb in circuit 1 is 40 02, and that in circuit 2 is 80 Q. Determine (a) the ratio 3₁/32 of the emfs and (b) the ratio 1₁/12 of the currents in the circuits. (c) If the speed of the rod in circuit 1 were twice that in circuit 2, what would be the ratio P₁/P2 of the powers in the circuits? (a) 1/2= Number i (b) 1₁1/12 = Number i (c) P₁/P₂= Number i X X X X X X X xLx X Units Units X Units X X x Conducting rail X X X X x x

An Alternating Current (AC) circuit has frequency v = 60 Hz. In such circuit there are 3 elements. The first one is a long thin solenoid with 4 × 104 turns/m, length of 10.0 cm and a cross-sectional area of 20.0 cm². The second one is a resistor with resistance R = 10.02. The third one is a parallel-plate capacitor is composed of two circular plates with radius 10.0 cmseparated by a gap of 0.05 mm. a) Calculate the angular frequency, w, of the circuit. b) Calculate the self inductance of such inductor and the inductive reactance. c) Calculate the capacitance of such device and the capacitive reactance. d) Draw the following functions on the same graph. Represent them as closely as possible to reality using the values you calculated so far. Use the graph on the back. IR cos (@t) VR IXL COS (@t+. VL = IXL COS VC = IXc cos wt- - - 元|2 元|2

In the circuit of the figure ℰ = 3.30 kV, C = 6.60 μF, R1 = R2 = R3 = 0.740 MΩ. With C completely uncharged, switch S is suddenly closed (at t = 0). At t = 0, what are (a) current i1 in resistor 1, (b) current i2 in resistor 2, and (c) current i3 in resistor 3? At t = ∞ (that is, after many time constants), what are (d)i1, (e)i2, and (f)i3? What is the potential difference V2 across resistor 2 at (g)t = 0 and (h)t = ∞?  Answer parts d, e, and f please