Chapter 2, Problem 2.14QAP

Interpretation Introduction

(a)

Interpretation:

The time it would take to discharge a 0.025 µF capacitor to 1% of its full charge through a resistance of 10 Mχ should be calculated.

Concept introduction:

The product of RC is referred to as time constant for the circuitand is a measure of the time required for a capacitor to chargeor discharge.

Capacitor is discharged to 1% of its full charge. Therefore, the value of charge at time ‘t’ can be related to the initial charge by following equation.

${\theta }_t=\frac{1}{100}\times {\theta }_0$

${\theta }_t$ = charge after discharge of the capacitor

${\theta }_0$ = initial charge of the capacitor

Time taken for the discharge of the capacitor can be calculated using following relationship;

${\theta }_t={\theta }_0{\text{ e}}^{-t/RC}$

Interpretation Introduction

(b)

Interpretation:

The time it would take to discharge a 0.025 µF capacitor to 1% of its full charge through a resistance of 1 Mχ should be calculated.

Concept introduction:

The product of RC is referred to as time constant for the circuit and is a measure of the time required for a capacitor to charge or discharge.

Capacitor is discharged to 1% of its full charge. Therefore, the value of charge at time ‘t’ can be related to the initial charge by following equation.

${\theta }_t=\frac{1}{100}\times {\theta }_0$

${\theta }_t$ = charge after discharge of the capacitor

${\theta }_0$ = initial charge of the capacitor

Time taken for the discharge of the capacitor can be calculated using following relationship;

${\theta }_t={\theta }_0{\text{ e}}^{-t/RC}$

Interpretation Introduction

(c)

Interpretation:

The time it would take to discharge a 0.025 µF capacitor to 1% of its full charge through a resistance of 1 kχ should be calculated.

Concept introduction:

The product of RC is referred to as time constant for the circuit and is a measure of the time required for a capacitor to charge or discharge.

Capacitor is discharged to 1% of its full charge. Therefore, the value of charge at time ‘t’ can be related to the initial charge by following equation.

${\theta }_t=\frac{1}{100}\times {\theta }_0$

${\theta }_t$ = charge after discharge of the capacitor

${\theta }_0$ = initial charge of the capacitor

Time taken for the discharge of the capacitor can be calculated using following relationship;

${\theta }_t={\theta }_0{\text{ e}}^{-t/RC}$