Electrical Transients

Problem 426: In a circuit consisting of a resistance, R ohms, in series with a capacitance, C farad, and connected to a DC source with emf E volts, the electrical charge, Q coulombs and the current i, amperes, maybe determined by solving the simultaneous equations: Ri + Q/C = E and I = dQ/dt. If R = 20 ohms, C = \(250\times10^{-6}\) farad and E = 100 volts, find i after a long time.

Problem 427: An 80 \(\mu\)F capacitor in series with a voltmeter of 10,000-ohm resistance is connected suddenly across a 100-V supply. How long will it take for the voltmeter to register 15 V?

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 429: An 80 \(\mu\)F capacitor in series with a 1000-ohm resistor is connected suddenly across a 110 V DC supply. Find the value of the current after one time constant.

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 431: A series RLC circuit with R = 1 k\(\Omega\), L = 1 H and C = 6.25 \(\mu\)F is suddenly connected across a 24 V dc source. At t = 0, I = 0 and q = 0. Determine the current after 0.01 sec.

Problem 432: A series RLC circuit has R = 200 \(\Omega\), L = 0.1 H and a capacitor C = 10 \(\mu\)F. If a 100 V dc source is connected across the end terminals of the series circuit at t = 0, determine the current after 1 millisecond. Assume zero initial conditions.

Problem 433: A series RLC circuit has R = 40 ohms, L =100 mH and C = 50 \(\mu\)F. The circuit is connected across a 100 V dc source at t = 0 through a switch. Determine the current 0.02 second after the switch is closed. Assume all initial condition to be zero.

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 435: A certain electric welder has a basic circuit equivalent to a series RL with R = 0.1 \(\Omega\) and L = 1 mH. It is connected to an AC source "e" through a switch "s" operated by an automatic timer, which closes the circuit at any desired point on the 60 cycle, sinusoidal wave "e". Calculate the magnitude of the transient current resulting when "s" closes as "e" is passing through its peak value of 100 volts.

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 437: A series RC circuit with R = 30 ohms and C = 250 \(\mu\)F is connected across an AC voltage source of emf 100 sin 100t through a switch. The switch is closed at t = 0. Determine the current when t = 0.01 second. Assume at t = 0, voltage across the capacitor is zero.

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 440: A series RL circuit has R = 10 ohms and L = 1 henry. The circuit is connected across a voltage source \(e(t)=10e^{-10t}\) through a switch that is initially open. The switch is closed at t = 0. Determine the current after 0.01 second. Assume initial current to be zero.

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.

What value of R is needed with a 0.05 μF capacitor for an RC time constant of 0.02 sec?