Electrical Transients

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 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 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 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 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 428: A 100 \(\mu\)F capacitor initially charged to 24 V is discharge across a series combination of a 1 k\(\Omega\) resistor and a 200 \(\mu\)F capacitor. Find the current after 1 sec.

Problem 430: 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. What is the initial rate of change of voltage across the resistor?

Problem 434: A 10-ohm resistance R and a 1.0-henry inductance L are connected in series. An AC voltage e(t) = 100 sin 377t is applied across the series circuit. The applicable differential equation is: Ri + L(di/dt) = e(t). Solve for the particular solution (without the complimentary solution) and determine the amplitude of the resulting sinusoidal current i(t).

Problem 436: Given the differential equation: L(di/dt) + Ri = 100 sin(377t) where L = 0.1 henry, R = 10 ohms and i(0) = 0. Determine the current at t = 0.01 second.

Problem 438: A series circuit has R = 10 ohms, L = 0.1 henry and C = 0.0001 farad. An AC voltage e = 100 sin 377t is applied across the series circuit. Solve for the particular solution (without the complimentary solution) and determine the amplitude of the resulting sinusoidal current i(t).

Problem 439: A 10-ohm resistance R and a 0.001 farad capacitance C are in series. An AC voltage e = 100 sin 377t is applied across the series circuit. Solve for the particular solution (without the complimentary solution) and determine the amplitude of the resulting sinusoidal current i(t).

Problem 441: The differential equation of a series RC circuit with DC applied voltage is: Ri + 1/C \(\int idt\) = E. If R = 50 ohms, C = 0.0001 farad, E = 100 volts and i(0) = 2.0 amperes, determine the Laplace transform expression for I(s).

Problem 442: A series RC circuit has R = 1k\(\Omega\) and C = 100 \(\mu\)F with an initial charge of 2000 \(\mu\)C. The combination is connected across a 100 V dc source and the switch is closed at t = 0. If the capacitor is connected in the circuit such that it will be discharging, determine the Laplace transform expression of the current drawn.

Problem 443: Determine the inverse Laplace transform of \(i_{(s)}=\dfrac{200}{s^2+50s+10625}\).

A coil having a resistance of 10 ohms and an inductance of 15 H is connected across a dc voltage of 150 V. When the supply is switched off, find the time for the current to drop to 9 A.