Question

A.)

In the lab, you will determine a value for the time constant of the RC circuit, by measuring the amount of time it takes the capacitor voltage to increase from 0.0 V to ______ % of its maximum value.

B.)

If you only have capacitors of one value, you can change the total capacitance of the circuit by using combinations of capacitors. Assuming that all the capacitors have the same value, how could you increase the total capacitance?

Options:

	add a resistor in parallel with the capacitor
	add a resistor in series with the capacitor
	add more capacitors in parallel with the first one
	add more capacitance in series with the first one

Answer 1

A)

The half-time of charging of capacitor is given by -

So, if we measure the time taken to increase the capacitor voltage from 0.0V to 50% of its maximum value, then we can use the above equation to get the time constant of RC circuit.

Hence the answer is = 50% of its maximum value.

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B)

The equivalent capacitance of the series combination of capacitors is given by -

If all the capacitors have same capacitance value 'C', then -

Which means that equivalent capacitance is -

Hence, the capacitance effectively decreases.

Now, the equivalent capacitance of parallel combination of capacitors is -

And if all the capacitors have same capacitance value, then -

So, note that the equivalent capacitance is larger than the individual capacitance.

Hence, option (c): add more capacitors in parallel with the first one is correct.

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