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Chapter 25: Q29P (page 742)

What capacitance is required to store energy of 10 kW.hat a potential difference of1000V?

Short Answer

Expert verified

The capacitance required to store energy of 10 kW.h is 72 F.

Step by step solution

01

The given data

a) The potential difference,V=1000 V .

b) Energy is stored in the capacitor, U =10 kW.h.

02

Understanding the concept of the energy stored in the capacitor

We use the relation of energy stored in the capacitor to find the capacitance C of the capacitor. We need to convert the given energy into joules.

Formula:

The energy stored by the capacitor is given by, U=12CV2 (i)

03

Calculation of the value of capacitance

The equation of the capacitance can be calculated using the given values in equation (i) as follows:

C=2UV2

Let’s convert the given value of energy in joules as:

U=10kW.h×103W1kW×3600s1h=10×103×3.6×103W.s=3.6×107W.s=3.6×107J

Substituting all values in (a), we get the value of capacitance as:

C=23.6×107J1000V2=7.2×107J106V2=72F

Hence, the value of the capacitance is 72 F.

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Most popular questions from this chapter

In Fig. 25-55,V=12V,C1=C5=C6=6.0μFandC2=C3=C4=4.0μF. What are (a) the net charge stored on the capacitors and (b) the charge on capacitor 4?

A parallel plate capacitor has plates of area0.12m2and a separation of 1.2 cm. A battery charges the plates to a potential difference of 120 Vand is then disconnected. A dielectric slab of thickness 4.0 mmand dielectric constant 4.8is then placed symmetrically between the plates.(a)What is the capacitance before the slab is inserted?(b)What is the capacitance with the slab in place?(c)What is free charge q before slab is inserted?(d)What is free charge q after slab is inserted?(e)What is the magnitude of electric field in space between plates and dielectric?(f)What is the magnitude of electric field in dielectric itself?(g)With the slab in place, what is the potential difference across the plates?(h)How much external work is involved in inserting the slab?

In Fig. 25-59, two parallelplatecapacitors Aand Bare connected in parallel across a 600 Vbattery. Each plate has area80.0cm2; the plate separations are 3.00 mm. Capacitor Ais filled with air; capacitor Bis filled with a dielectric of dielectric constant k = 2.60. Find the magnitude of the electric field within (a) the dielectric of capacitor Band (b) the air of capacitor A.What are the free charge densitiesσon the higher-potential plate of (c) capacitor Aand (d) capacitor B? (e) What is the induced charge densityon the top surface of the dielectric?

(a) In Fig. 25-19a, are capacitors 1 and 3 in series? (b) In the samefigure, are capacitors 1 and 2 in parallel? (c) Rank the equivalent capacitances of the four circuits shown in Fig. 25-19, greatest first.

Figure 25-20 shows three circuits, each consisting of a switch and two capacitors, initially charged as indicated (top plate positive). After the switches have been closed, in which circuit (if any) will the charge on the left-hand capacitor (a) increase, (b) decrease, and (c) remain the same?
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