Question

If R and C be the resistance and capacitance
respectively, then prove that unit of RC is second. ​

Answer 1

Explanation:

We know that Capacitance can be written as;

C  = Charge / Potential = Q/V

And we can write resistance as;

R = V/I ( Ohm’s law )

Now

Charge or Q = current x time = I x T

C =  Q/V = I x T / V

Now multiply R and C ;

R x C = (I x T / V) x V/I =T

Unit of time is sec, hence product of RC has unit of sec

Answer 2

The unit of RC is second.

Explanation:

Resistance:

According to Ohm's law,

R = V/I

Where,

R = Resistance in Ohms

V = Potential difference in Volts

I = Current in Ampere

$R = \frac{V\times t}{Q}$

Where,

t = time in seconds

Q = Charge in Columb

Capacitance:

Capacitance is expressed in Farad. It is the ratio of charge to potential difference.

$C=\frac{Q}{V}$

Product of resistance and capacitance:

$RC=\frac{V \times t}{Q} \times \frac{Q}{V}$

$RC=t$

Thus, time is in seconds.

Hence proved.