Question

Verify that the time constant RC has units of time.

Short answer

The time constant RC has units of time.

Step-by-step solution

Time constant

The time constant for a capacitor is the time required by the capacitor to charge to 63.2 % of the applied voltage in the given circuit. it has the unit of time (s).

Step 2:Calculation of the unit of time constant

The self-capacitance of a conductor is;

$C=\frac{q}{\epsilon }$

Here

• The charge has a unit of coulomb (C)
• Potential has a unit of a volt (V)
• Capacitance has a unit of Farad (F);

The above expression can be written as:

$C_{unit}=\frac{C}{V}$

Resistance of a conductor is:

$R=\frac{\epsilon }{l}$

Here,

• The resistance unit is ohm’s $\left(\Omega \right)$and
• the current unit is Coulomb (C) per second.

The above expression can be written as:

$R_{unit}=\frac{V}{C/s}$

From the above two equations, we can calculate the unit of time constant as:

$$\begin{gathered} {\left(RC\right)}_{unit}=R_{unit}\times C_{unit} \\ =\frac{V}{C/s}\times \frac{C}{V} \\ =s \end{gathered}$$

Hence, the time constant RC has units of time (s).