Question

Two students measure the time constant of an RC circuit. The first student charges the capacitor using a 12 V battery, then lets the capacitor discharge the resistor. The second student repeats the experiment using a 5 V battery. Which student measures the longer time constant? Why? Select the correct answer and explanation.a.) The second student gets a greater time constant, since the time constant decreases as the charge on the capacitor increases.b.) The first student gets a greater time constant, since the time constant increases as the charge on the capacitor increases.c.) Both students get the same time constant, since the time constant does not depend on the charge on the capacitor.

Answer 1

b.) The first student gets a greater time constant, since the time constant increases as the charge on the capacitor increases.

Answer 2

a)

Step-by-step explanation:

The time constant is given by

`\tau=RC`

Where R is the resistance of the circuit, and C is the total (connected) capacitance. Furthermore we have that:

`\tau=R(Q)/(V)\\\tau_1=(1)/(12)(Q)/(V)\\\tau_2=(1)/(5)(Q)/(V)`

Hence, the time constant measured by the second student is greater than the time constant measured by the first one.

Answer

a) The second student gets a greater time constant, since the time constant decreases as the charge on the capacitor increases

hope this helps!