Question

prove that T = RC....?​

Answer 1

Answer:

If Q represemts charge in coloumbs, t represents time in seconds than, C is capacitance in Farads than by ohms law

R=V/I=V*t/Q

and

C=Q/V

gives

R*C = (V*t/Q)* (Q/V)=t

so t has units of secons

Explanation:

hope it is help full for you

Answer 2

The correct question: The time constant of a series RC circuit is t = RC. Verify that an ohm times Farad is equivalent to second.

The correct answer is given below.

Given:

The time constant of a series RC circuit, t = RC.

To Find:

We have to verify that an ohm times Farad is equivalent to second.

Solution:

Given that, t = RC.

From Ohm's law,

$V = IR$,

where V is the voltage in Volt, R is the resistance in Ω, and I is the current in Ampere.

Let this be equation (1).

The equation for current is given by,

$I = \frac{Charge}{Time} = \frac{q}{t}$.

On substituting this equation for the current in equation (1), we get,

$V = \frac{q}{t} .R$

On rearranging the above equation, it becomes,

$R = V. \frac{t}{q}$

Introducing capacitance (C) to the above equation we get,

$RC = V. \frac{t}{q}.C$

$i.e., RC = Vt.\frac{C}{q}$

Let this be equation (2).

Using the relation $q = CV$, we get that $\frac{q}{C} = V$.

∴, $\frac{C}{q} = \frac{1}{V}.$

Substituting this in equation (3), we  get,

$RC = Vt.\frac{1}{V}$

$i.e., t = RC.$

Hence, it is verified that an ohm times Farad is equivalent to second.

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