Capacitor Voltage-Current Relations

      A series RC circuit is designed with a variable voltage in its input. In the series circuit total

current is equal with resistor current, and also it is equal with the capacitor current.

Part a: a sinusoidal wave, V(t), with frequency = 1 KHz, and amplitude  = 2v, and offset = 0v is

connected to the input of a RC circuit. R = 100 Ω  , C = 1 μF

Figure 1: An sinusoidal Input with f = 1 KHz , Vin = 2V

According to the figure 1, one cycle is equal with 1 ms, this is period of sinusoidal wave. So f = 1/T,

f = 1 KHz. Channel 1 of oscilloscope (C1) shows the resistor voltage difference, and channel 2 (C2)

shows the capacitor voltage difference. Of course, the circuit current is in phase with the resistor

voltage difference, but the capacitor voltage difference is 90 degree lag of the circuit current.

Therefore, according to the figure 1, C2 is started at maximum and C1 is stared at zero. This show 90

degree difference between current and voltage of the capacitor.

Figure 2: Schematic of  a Series RC circuit

Figure 3: An sinusoidal Input with f = 2 KHz , Vin = 2V

Part b: a sinusoidal wave, V(t), with frequency = 2 KHz, and amplitude  = 2v, and offset = 0v is

connected to the input of a RC circuit. R = 100 Ω  , C = 1 μF

Figure 4: A Triangle Input Voltage f = 100 Hz, Amplitude = 4v

According to the figure 4, one cycle is equal to 10 ms, so f = 1/T, f = 1/ 0.01 s , f = 100 Hz

A triangular input voltage with frequency = 100 Hz, and amplitude = 4v, and offset 0v is connected

to the series RC circuit. The resistor voltage and current is triangular (channel 2, C2), and also the

total current is triangular shape. The capacitor voltage is square (channel 1, C1) because derivative

of a square function is a triangle function.