   Chapter 18, Problem 65AP

Chapter
Section
Textbook Problem

What are the expected readings of the ammeter and voltmeter for the circuit in Figure P18.65? Figure P18.65

(a)

To determine
The magnitude of the current in the resistor after 9.0μS when the resistor is connected between the terminals of the capacitor.

Explanation

Given Info:

The capacitance of the capacitor is 2.0nF .

The initial charge of the capacitor is 5.10μC .

The total time that the resistor is connected in the circuit is 9.0μS .

The resistance in the circuit is 1.3 .

Explanation:

The remaining charge in the capacitor at the time t is,

q=Q0etτ (I)

• τ is the time constant of the RC circuit
• t is the time that the switch is closed
• Q0 is the initial charge of the capacitor

Since, the time constant of the RC circuit is,

τ=RC (II)

• R is the resistance of the circuit
• C is the capacitance of the capacitor in the circuit

Formula to calculate the total potential difference across the capacitor at time t is,

ΔV=qC

• q is the remaining change across the capacitor at time t

Re-write the equation (III) using equations (I) and (II),

ΔV=Q0etRCC

Thus, The expression for potential difference across the capacitor is, ΔV=Q0etRCC .

Conclusion:

From section 1,

The expression for potential difference across the capacitor is, ΔV=Q0etRCC .

According to the Kirchhoff’s loop rule,

ΔViR=0

Thus,

Formula to calculate the current through the resistor is,

i=ΔVR=Q0etRCRC

Substitute 5

(b)

To determine
The charge remains in the capacitor after a 8.0μS .

(c)

To determine
The maximum current in the resistor.

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