1. Suppose that you have two identical capacitors and a single resistor. If you

Question

1.

Suppose that you have two identical capacitors and a single resistor. If you make an RC circuit with one capacitor and the resistor it turns out that the time constant is 4.8ms. Now you rebuild the circuit but instead of putting in just the one capacitor, you put in the pair of capacitors connected in parallel. What is the time constant for this circuit?

2.

Suppose that you have two identical capacitors and a single resistor. If you make an RC circuit with one capacitor and the resistor it turns out that the time constant is 5.4ms. Now you rebuild the circuit but instead of putting in just the one capacitor, you put in the pair of capacitors connected in series. What is the time constant for this circuit?

3.

I want to make a timing circuit. Remember that the voltage drop across the capacitor is VPower Supply - VResistor. Thus, as the voltage drop across the resistor decreases, the voltage drop across the capacitor increases. My timing circuit is supposed to tell my windshield wiper motor to sweep the blades. I want to be able to easily change it to start a sweep every 2, 4, 8, or 16 seconds. The heart of this is an RC circuit. The supply voltage is 12.0V. When the voltage across the capacitor reaches 3.0V the sweep will start, the the capacitor will be discharged, and the cycle will start anew. Suppose that the size of the capacitor is 1.0mF. What four resistor values should I have available at the turn of a knob to get the timing right?

Explanation / Answer

1) Time constants in RC circuits = R*C

When you put the similar capacitancei in parallel then net capacitance = 2C

hence time constant new value will be 4.8*2 = 9.6ms

2) The capacitance will decrease in series

hence time constant will reduce by a factor of 2, new time constant = 2.7 ms

3) RC = 2

hence R = 2k ohms

RC = 4

hence R = 4K ohms

RC = 8

hence R = 8k ohms

RC = 16

hence R = 16K ohms

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