Question

Each of the circuits below consists of identical batteries, resistors, and capacitors.

a) The time constant is longer in circuit A.
b) The time constant is longer in circuit B.
c) The time constants are equal.
d) The time constants cannot be determined without additional information.

Answer 1

The time constant for an RC circuit depends on the resistance and capacitance values. By comparing the values in circuit A and circuit B, we can determine which circuit has a longer time constant.

Step-by-step explanation:

The time constant for an RC circuit is given by the formula T = RC, where T is the time constant, R is the resistance, and C is the capacitance. In circuit A, the time constant can be determined by multiplying the resistance and capacitance values.

Similarly, in circuit B, the time constant can be calculated using its resistance and capacitance values. By comparing the resistance and capacitance values in both circuits, we can determine which circuit has a longer time constant.

For example, if the resistance value is higher in circuit A compared to circuit B, while the capacitance values are the same, then the time constant in circuit A will be longer. On the other hand, if the capacitance value is higher in circuit B compared to circuit A, while the resistance values are the same, then the time constant in circuit B will be longer.

If the resistance and capacitance values are equal in both circuits, then the time constants will also be equal.