For the circuit shown below, where R = 5.3 kΩ, and L = 41.9 mH, 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.

For the circuit shown below, where R = 7.2 kΩ, and C = 9.5 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 = 75.4 and x = 12, find the magnitude of the AC steady state voltage at the output (v_O), to 1% 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 = 1.5 ...

... 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 = 100 nF and L = 100 mH?

If the damping factor (α) for a particular circuit is equal to 1/sqrt(L.C), 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 a governing differential equation for an RLC circuit as shown below:

Find the value of the damping ratio (ζ), if R = 10k Ω, L = 6.3 mH and C = 6.1 μF, to 1% accuracy.

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

Write out the KVL indicated in this circuit, in terms of the current (i), source voltage (vS), R, C and L, for t > 0.

Your answer might look something like: C.d^2(i)/dt^2 + di/dt + R.i = vS/L

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

Find the particular solution for vR for this equation (i.e. vC 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 = 8.5 kΩ, C = 2 μF.

For the circuit shown below ...

... find the value of f(t), given R = 9.6 kΩ, L = 3.4 mH, in the equation ...

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