Engineering Max Voltage Across Capacitor & Resistor in a Circuit

[GalMichaeli]

Homework Statement

For the circuit in the picture below, with V_{c}(t=0) = 0 and a voltage source with period T described by
V_s(t) = \sum_{-\infty}^\infty (-1)^{n}g(t-nT)
where
g(t) = 7[u(t)-u(t-T)]\quad [Volt]
and u(t) is a step function described by
<br /> u(t) =<br /> \begin{cases}<br /> 1 &amp; \text{if } t \geq 0 \\<br /> 0 &amp; \text{if } t &lt; 0<br /> \end{cases}<br />
What is the maximal voltages across the capacitor?
What is the maximal voltages across the resistor?

Homework Equations

The Attempt at a Solution

The voltage source is a pulse train with amplitude \pm 14 \quad [Volts] and since at time t = 0 we may consider the cap. as a short-circuit, we have V_{R}(t=0) = 14 \quad [Volts].
I'm having trouble figuring out what the maximal voltage across the cap. is.
Should I apply transient analysis?

Thanx.

 

[rude man]

First, never mind the voltage anywhere at t=0. You don't know what t=0 is. This voltage wavetrain has been running since t = -∞.

Now my gut reaction was Fourier series. But that's the hard way. Instead:

1. realize that v(t), the voltage across C, will vary symmetrically about zero volts since that is the average value of your input, from Vmin to Vmax = |Vmin|.

2.Then realize that the most negative C voltage is just before the input goes from -E to +E (why?). Then realize by symmetry that the max C voltage will occur just before the input transitions from +E to -E (again, be able to justify this statement).

3. Write the KVL: current thru R = current into C starting with t=0 at the -E to +E input transition. This will be a differential equation, easy to solve, in capacitor voltage v(t). Solve with the initial condition v(0+) = Vmin, then solve for v(T) = Vmax. The rest should "follow immediately" as the textbooks say.