Learning Resource Topics Overview 1 Charge & Coulomb’s Law 2 Electric Current 3 Voltage 4 Resistance 5 Ohm’s Law 6 Power & Energy 7 Elements of Electric Circuits 8 Kirchhoff’s Law 9 Series Circuits 10 Parallel Circuits 11 Analysis of Combination Circuits 12 Capacitance 13 Inductance

# Exercise

Consider a capacitor of 10 µF.

What is the voltage across the capacitor when the current through it is shown graphically in Figure 12.4?

Figure 12.4 The current waveform through a capacitor.

Type your solution in the box below:

Solution: Using Equation (12.8)

The difference between the values of the voltage at t and t0 is proportional to the area under the current curve between these same two values of time. The proportionality is 1/C.

Let us start our starting point t0 prior to zero time at -. From the current waveform, it is clear that no current has ever been applied to the capacitor since the beginning of time

Accordingly, the integral of the current (first equation) between t0 = - and 0 is simply zero. Since i = 0 in that interval, thus,

or

Now consider the time interval represented by the rectangular pulse

Since v(0) = 0

Accordingly

Graphical Representation

Figure 12.5 Graphical representation

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