At the moment, t = 0, a switch is closed and a 24.0-V battery is connected to a

Question

At the moment, t = 0, a switch is closed and a 24.0-V battery is connected to a 5.00-mH coil and 6.00 ? resister in series. Draw a

figure of this circuit.

a) Immediately after the switch is closed, how does the potential difference across the resistor compare to the emf across the

coil?

b) Answer the same questions about the circuit several seconds later.

c) Is there an instant at which these two voltages are equal in magnitude? If so, when? Is there more than one such instant?

Provide a sketch that includes the voltages across the resistor and inductor as a function of time.

d) After a 4.00-A current is established in the resistor and coil, the battery is suddenly replaced by a short circuit. Draw a

schematic diagram of this circuit that includes a switch. Answer part a, b, and c again with reference to this new circuit

Explanation / Answer

V[orig] = 24 V ; L = 0.005 H ; R = 6 ohm ; ? = L / R = 0.0008333

a] Immediately after, the voltage across the resistor is 0; the emf across coil is 24 V.

b] Several seconds later, the voltage across resistor is 24 V; the emf across coil is 0.

c] V[induc] = V[resistor] = V[orig] / 2 = 12 V
V[induc] (t) = Vo*e^( -t/? ) ? 12 V = (24 V) * e^( -t / 0.0008333 ) ? t = 0.000578 sec

d] As current deteriorates, voltage across the resistor is always equal to emf across coil.

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