Chapter 18, Problem 59AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A voltage ΔV is applied to a series configuration of n resistors, each of resistance R. The circuit components are reconnected in a parallel configuration, and voltage ΔV is again applied. Show that the power consumed by the series configuration is 1/n2 times the power consumed by the parallel configuration.

To determine
The charges q1 and q2 on capacitors C1 and C2 after the switch is closed as a function of time.

Explanation

Given Info:

The first resistance R1 is 2.0â€‰kÎ© .

The second resistance R2 is 3.0â€‰kÎ©

The first capacitance C1 is 2.0â€‰Î¼F .

The second resistance C2 is 3.0â€‰Î¼F

The total resistance in the circuit is 1.2â€‰kÎ© .

The total capacitance in the circuit is 5.0â€‰Î¼F .

The total capacitance in the circuit is 5.0â€‰Î¼F .

The emf of the battery is 120.0â€‰V .

Explanation:

Since, the resistances are in parallel connection,

Formula to calculate the total resistance is,

R=11R1+1R2

• R1 is the first resistance
• R2 is the second resistance

Substitute 2.0â€‰kÎ© for R1 and 3.0â€‰kÎ© for R2 to find the total resistance of the circuit,

Thus, the total resistance in the circuit is 1.2â€‰kÎ© .

Since, the capacitances are in parallel connection,

Formula to calculate the total capacitance is,

C=C1+C2

• C1 is the capacitance of the first capacitor
• C2 is the capacitance of the second capacitor

Substitute 2.0â€‰Î¼F for C1 and 3.0â€‰Î¼F for C2 to find the total capacitance of the circuit,

C=2.0â€‰Î¼F+3.0â€‰Î¼F=5.0â€‰Î¼F

Thus, the total capacitance in the circuit is 5.0â€‰Î¼F .

Formula to calculate the time constant of the circuit is,

Ï„=RC

• R is the total resistance of the circuit
• C is the total capacitance of the circuit

Substitute 1.2â€‰kÎ© for R and 5.0â€‰Î¼F for C to find the time constant of the circuit,

Thus, the time constant of the circuit is 6.0â€‰s1000 .

Formula to calculate the maximum charge is,

Qmax=CÎµ

• Îµ is the emf of the battery
• C is the total capacitance of the circuit

Substitute 5

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