For the circuit shown below, where R = 4.4 kΩ, and C = 7.8 μF, and the source is sinusoidal with an angular frequency (ω) of 1 k rad/s:

Calculate the value of the real part of the equivalent impedance of the circuit connected to the load, in SI units, to 1% accuracy.

The following circuit is driven by a sinusoidal source. Given values of y = 58.4 and x = 45.7, find the angle of the AC steady state voltage at the output (v_O), in degrees, to 0.5^o accuracy.

For the circuit shown below, which is driven by a sinusoidal voltage source with an amplitude of 1V at 0 degrees phase, where x = 0.2 ...

... what must the angular frequency of the source (ω - in rad/s, accurate to 1%) such that the AC steady state output voltage (vO) has an amplitude of 1/sqrt(2) at a phase of +45^o? (hint: i.e. |zL| = |zR|)

For a circuit with a governing differential equation as shown below:

Is the circuit over-, under-, or critically damped, if R = 1 kΩ, C = 10 nF and L = 100 mH?

If the damping ratio (ζ) for a particular circuit is less than 1, what are the roots for DE that governs the circuit?

I.e. if the roots for the DE can be found from:

what is λ={λ₁,λ₂} given the above conditions?

Given the circuit shown below, the switch moves from position 1 to position 2 at just before t=0.

Write out the KCL indicated in this circuit, in terms of the voltage (v{R,L,C}), source current (iS), R, C and L, for t > 0.

Your answer might look something like: C.d^2(v)/dt^2 + dv/dt + R.v = iS/L

Given a governing differential equation for a circuit as shown below:

Find the particular solution for i for this equation (i.e. i where t goes to infinity), given vS = u(t) V (u(t) is the unit step function, 0 before t=0, 1 for t=0 and beyond), for t>0, to 1% accuracy. The component values are R = 3.3 kΩ, L = 2.1 mF.

For the circuit shown below ...

... find the value of f(t), given R = 1.8 kΩ, C = 1 μF, in the equation ...

... in SI units, to 1% accuracy.

Given the circuit below is driven by a 50 Hz sinusiod with a magnitude of 240 volts and a phase of 0^o, find the magnitude of the current through this circuit (i_O), in SI units, accurate to 1%.

The inductor impedances are set by x = 1.8 and y = 12.

For the circuit shown below, where R = 4.4 kΩ, and C = 5.8 μF, and the source is sinusoidal with an angular frequency (ω) of 1 k rad/s:

Calculate the value of the imaginary part of the equivalent impedance of the circuit connected to the load, in SI units, to 1% accuracy.