Given the RC circuit below, where the voltage source is providing a square wave with a low level of 0 V and a high level of 1 V as shown on the plot below:

If we assume that at t=0, vC(0)=0, and that the inhomogeneous differential equation that governs vC is dVc/dt +vC/CR = vS/CR:

Find the particular solution (vP) for vC, for 0<t<T/2, to better than two sig. figures (Hint: this should be a real number).

Your answer may look like: vP = 0.165 V, for example.

Given the RC circuit below, where the voltage source is providing a square wave with a low level of 0 V and a high level of 1 V as shown on the plot below:

If we assume that at t=0, vC(0)=0, and that the inhomogeneous differential equation that governs vC is dVc/dt +vC/CR = vS/CR:

Find the solution for vC to the homogeneous part of this equation (dVc/dt +vC/CR =0). Please use 'K' for any constant of integration you find ...

Given the RC circuit below, where the voltage source is providing a square wave with a low level of 0 V and a high level of 1 V as shown on the plot below:

The homogeneous differential equation that describes the voltage over the capacitor (v_C) is dvC/dt + f.vC = g.vS.

Given the RC circuit below, where the voltage source is providing a square wave with a low level of 0 V and a high level of 1 V as shown on the plot below:

Find the homogeneous differential equation that describes the voltage over the capacitor (vC). A homogeneous DE will have the form dy/dx +y.f(x) = 0, and can be found from an equation of the form dy/dx +y.f(x) = g(x) by setting g(x)=0.

The governing KCL for this circuit is C.dvC/dt = (vS-vC)/R.

An example solution might look like: dVc/dt - C/Vc = 0

Given the RC circuit below, where the voltage source is providing a square wave with a low level of 0 V and a high level of 1 V as shown on the plot below:

Write the KCL for the node 'vC', in terms of capacitor voltage (vC), source voltage (vC), resistance (R) and capacitance (C).

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 angle of the current through this circuit (i_O), in degrees, accurate to 0.5^o.

The inductor impedances are set by x = 1.6 and y = 18.2.

For the circuit shown below, where R = 3.1 kΩ, and L = 48 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 = 0.18 kΩ, and L = 42.2 mH, 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.

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

Is the circuit over-, under-, or critically damped, if R = 2 kΩ, C = 10 μF and L = 100 mH?

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 ...

... 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. |zC| = |zR|)