Chapter 7, Problem 1RQ

An RC circuit has R = 2 Ω and C = 4 F. The time constant is:

(a)    0.5 s

(b)    2 s

(c)    4 s

(d)    8 s    15 s

To determine

Choose the correct option to find the time constant for an RC circuit.

Answer to Problem 1RQ

The correct option from the given choices is (d) 8 s.

Explanation of Solution

Given data:

The value of resistance $\left(R\right)$ is $2\Omega$.

The value of capacitance $\left(C\right)$ is $4\text{F}$.

Formula used:

Write the expression to calculate the time constant for RC circuit.

$\tau =RC$ (1)

Here

R is the resistance of the resistor,

C is the capacitance of the capacitor.

Calculation:

Substitute $2\Omega$ for $R$ and $4\text{F}$ for $C$ in equation (1) to find the time constant $\tau$.

$\tau =\left(2\Omega \right)\left(4\text{F}\right)$ (2)

Substitute the units $\frac{\text{V}}{\text{A}}$ for $\Omega$ and $\frac{\text{A}\cdot \text{s}}{\text{V}}$ for F in equation (2) to find the time constant $\tau$ in seconds.

$\begin{array}{c}\tau =\left(2\frac{\text{V}}{\text{A}}\right)\left(4\frac{\text{A}\cdot \text{s}}{\text{V}}\right)\\ =8\text{s}\end{array}$

The time constant for an RC circuit is $8\text{s}$. Therefore, the option (d) is correct and the options (a), (b), (c), (e) are incorrect.

Conclusion:

Thus, the correct option from the given choices is (d) 8 s.