Question

A 100 µF capacitor that had been charged to 30 V is discharged through a resistor. The figure shows the capacitor voltage as a function of time.

What is the value of the resistance?

R= ?? O

I already tried 1.8 x 104 but that was not right.

A 100 muF capacitor that had been charged to 30 V is discharged through a resistor. The figure shows the capacitor voltage as a function of time.What is the value of the resistance? R= ?? O I already tried 1.8 x 104 but that was not right.

Answer 1

Concepts and reason

The main concept of this question is resistance connected in circuit consisting of resistance, capacitance and a dc battery connected in series combination.

The resistance can be found by using the expression for the voltage in the circuit.

Fundamentals

Consider a circuit consisting of resistance R and capacitor C connected in series to battery.

The expression for resistance in the circuit is,

Here, V is the voltage of in the circuit at any time t and is the initial voltage across the capacitor.

(a)

The expression for the voltage V in the circuit at any time t is,

Solve it for resistance in the circuit as follows:

Take natural logarithm on both the sides,

Rewrite the equation for resistance R as follows:

The expression for resistance R in the circuit is,

Substitute for C, for for V and for t .

Ans: Part a

The magnitude of resistance in the RC circuit is .