Electrical Transients

Problem 406: In an RL circuit, Kirchhoff's Law gives the following relation: E = L di/dt + Ri where: E = supply voltage (200 volts), R = resistance (20 ohms), L = inductance (1 henry), t = time in seconds, i = current in amperes. If i = 0 when t = 0, find i when t = 0.02 second.

Problem 407: In an RL circuit, Kirchhoff's Law gives the following relation: E = L di/dt + Ri where: E = supply voltage (200 volts), R = resistance (20 ohms), L = inductance (1 henry), t = time in seconds, i = current in amperes. If i = 0 when t = 0, find i after a long time.

Problem 408: A 6.0 H coil whose resistance is 12 ohms is connected in series with a 24 ohms resistor and to a 144 V battery and a switch. The switch is closed at t = 0. Determine the time constant of the circuit.

Problem 409: The current in a coil decays as follows: when t = 0.002 sec, the current is 10 mA; when t = 0.006 s, the current drops to 4 mA. The time constant of the coil is ___.

Problem 410: A time of 10 milliseconds is required for the current on a series RL dc circuit to reach 90% of its final steady state value. Assume at t = 0, i(0) = 0. What is the time constant in seconds for the circuit?

Problem 411: A coil has a resistance of 10 ohms and a time constant of 1 second. If the coil connected across a steady potential of 24 V, how much is the current after 2 ms?

Problem 412: The shunt winding of a machine has a resistance of 80 ohms and an inductance of 4 H is suddenly switched on to a 220-V supply. Find the time taken for the current to rise to half its steady state value.

Problem 413: A dc voltage E is applied across an RL circuit at t = 0. At what time after, is the voltage across the resistor equal to that across the inductor?

Problem 414: A 500-ohm relay coil has an inductance of 10 mH. This relay requires a current of 40 mA in order to trigger. How long after the switch is closed will the relay trigger if a 24 V DC source is applied across its terminals. Assume at t = 0, i = 0.

Problem 415: A 6.0 H coil whose resistance is 12 ohms is connected in series with a 24 ohms resistor and to a 144 V battery and a switch. The switch is closed at t = 0. Determine the current at t = 0.1 second.

Problem 416: A coil having a resistance of 10 \(\Omega\) and inductance of 10 H is connected in series with a 15 \(\Omega\) resistor. A 200-V DC source is connected to the circuit at t = 0. Determine the voltage across the coil at t = 0.05 sec.

Problem 417: A series RL circuit is connected across a dc source through a switch. Three (3) milliseconds after the switch is closed, the voltage across the inductance is 20 V and drops to 5 V after 20 ms. If R = 100 ohms, find L. Assume at t = 0, I = 0.

Problem 418: A 1\(\Omega\) resistor is connected in series with a 2-mH inductor. If a 12-V dc source is suddenly connected across its terminals, how long will it take, such that the voltage across the resistor will be twice as that of the inductor.

Problem 419: A resistance of 100 k\(\Omega\) is connected in series with a 100 \(\mu\)F capacitor. If the combination is suddenly connected across a 125 V DC source, determine the current one second after the switch is closed.

Problem 420: An uncharged condenser in series with a 120-volt voltmeter of 10,000 ohms resistance is suddenly connected to a 100 V battery. One second later, the voltmeter reads 60 volt. Determine the capacitance of the condenser.

Problem 421: A 120 \(\mu\)F capacitor has an initial charge of 600 \(\mu\)C. It is discharged through a 40 \(\Omega\) resistor. How long will it take in order for the capacitor to discharge to 150 \(\mu\)C.

Problem 422: A 50 \(\mu\)F capacitor is connected across a 400 V dc source. It is then discharged through a voltmeter whose resistance is 100-k\(\Omega\). How long will it take for the capacitor to discharge to 1.8 J of stored energy?

Problem 423: A 20-ohm resistance R and a 0.001 farad capacitance C are in series. A direct current voltage E of 100 volts is applied across the series circuit at t = 0 and the initial current i(0) = 5 A. The applicable differential equation is: R(di/dt) + i/C = 0. Solve the differential equation and determine the resulting current i(t) at t = 0.01 second.

Problem 424: A series RC circuit consist of R = 2 M\(\Omega\) and an uncharged capacitor C = 5 \(\mu\)F. The circuit is connected across a 100 VDC source at t = 0. Determine the voltage across the resistor 5 seconds later.

Problem 425: An uncharged condenser in series with a 120-volt voltmeter of 10,000 ohms resistance is suddenly connected to a 100 V battery. One second later, the voltmeter reads 60 volt. Determine the rate at which the voltage across the condenser is charging.