Answered: 4.0 4.0 3.0 Cea 8.0 8.0 V2 (b) (c) (d)…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter21: Circuits And Dc Instruments

Section: Chapter Questions

Problem 35CQ: When discharging a capacitor, as discussed in conjunction with Figure 21.39, how long does it take...

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Conceptualize Study figure (a) carefully and make sure you understand how the capacitors are connected.

Categorize Figure (a) shows that the circuit contains both series and parallel connections, so we use the rules for series and parallel combinations discussed in this section.

Analyze Reduce the combination step by step as indicated in the figure.

The c₁ = 1.1 µF and 3.0 µF capacitors in figure (a) are in parallel. Find the equivalent capacitance:

C_eq = C₁ + C₂ = 4.1 µF (top red circles)

The c₂ = 2.0 µF and 6.0 µF capacitors in figure (a) are also in parallel:

C_eq = C₁ + C₂ = 8.0 µF (bottom red circles)

The circuit now looks like figure (b). The two capacitors in the upper branch are in series. Find the equivalent capacitance:

C_eq

C₁

C₂

4.0µF

4.1µF

(top green circles)

C_eq = 2.0 µF

The two capacitors in the lower branch are also in series. Find the equivalent capacitance:

C_eq

C₁

C₂

8.0µF

(bottom green circles)

C_eq = 4.0 µF

The circuit now looks like figure (c). The 2.0 µF and 4.0 µF capacitors are in parallel:

C_eq = C₁ + C₂ = µF

Finalize This final value is that of the single equivalent capacitor shown in Figure (d). For further practice in treating circuits with combinations of capacitors, imagine that a battery is connected between points a and b so that a potential difference ΔV is established across the combination. Can you find the voltage across and the charge on each capacitor?

MASTER IT HINTS: GETTING STARTED | I'M STUCK!

Consider three capacitors having capacitances of 5.3 µF, 6.42 µF, and 2.38 µF. Find their equivalent capacitance if they are connected as follows.

(a) in parallel
C_eq = µF

(b) in series
C_eq = µF

4.0
4.0
3.0
Cea
8.0
8.0
V2
(b)
(c)
(d)
To find the equivalent combination of the capacitors in (a), the various combinations are
reduced in steps as indicated in (b), (c), and (d), using the series and parallel rules described
in the text. All capacitance values are in microfarads.

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