What capacitance is needed to store \(3.00{\bf{ }}\mu C\) of charge at a voltage of \(120\;V\)?

Short Answer

Expert verified

\(2.50 \times {10^{ - 8}}\;F\) capacitance is needed to store \(3.00{\rm{ }}\mu C\) of charge at a voltage of \(120\;V\).

Step by step solution

01

Defining capacitor

A capacitor is a device used to store electrical energy and works in an electric field. It is a passive electrical component with two terminals. Capacitance is the term used to describe the effect of a capacitor.

02

Work of Capacitor and Information Given

Any pair of conductors separated by an insulating substance is referred to as a capacitor. When the capacitor is charged, the two conductors have charges of equal magnitude\(Q\)and opposite sign, and the positively charged conductor's potential\(\Delta V\)with respect to the negatively charged conductor is proportional to\(Q\)The ratio of\(Q\)to\(\Delta V\)determines the capacitance\(C\)

\(C = \frac{Q}{{\Delta V}}\)

The farad is the SI unit of capacitance (\(F\)):\(F = 1C/V\)

The capacitor holds the following charge:

\(\begin{array}{c}Q = (3.00{\rm{ }}\mu C)\left( {\frac{{1{\rm{ }}C}}{{{{10}^6}{\rm{ }}\mu C}}} \right)\\ = 3.00 \times {10^{ - 6}}{\rm{ }}C\end{array}\)

Across the capacitor, the potential difference is \(\Delta V = 120\;V\).

03

Value of the capacitor

The capacitor's capacitance is:

\(C = \frac{Q}{{\Delta V}}\)

Substitute the values of\(Q\)and\(\Delta V\):

\(\begin{array}{c}C = \frac{{3.00 \times {{10}^{ - 6}}{\rm{ }}C}}{{120\;V}}\\ = 2.50 \times {10^{ - 8}}\;F\end{array}\)

Therefore, the capacitance needed is \(2.50 \times {10^{ - 8}}\;F\).

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Most popular questions from this chapter

Integrated Concepts

A \(12.0\;V\)battery-operated bottle warmer heats \(50.0\;g\)of glass, \(2.50 \times {10^2}{\rm{ }}g\)of baby formula, and \(2.00 \times {10^2}\;g\)of aluminium from \({20.0^\circ }C\) to \({90.0^\circ }C\).

(a) How much charge is moved by the battery?

(b) How many electrons per second flow if it takes \(5.00\)min to warm the formula? (Hint: Assume that the specific heat of baby formula is about the same as the specific heat of water.)

Unreasonable Results

(a) Find the voltage near a \(10.0\;cm\) diameter metal sphere that has \(8.00{\rm{ }}C\) of excess positive charge on it.

(b) What is unreasonable about this result?

(c) Which assumptions are responsible?

A research Van de Graaff generator has a \(2.00 - m\)-diameter metal sphere with a charge of \(5.00{\rm{ }}mC\) on it. (a) What is the potential near its surface? (b) At what distance from its centre is the potential \(1.00{\rm{ }}MV\)? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generator. What is its energy in \(MeV\)at this distance?

The naturally occurring charge on the ground on a fine day out in the open country is \( - 1.00n{\rm{ }}C/{m^2}\).

(a) What is the electric field relative to ground at a height of \(3.00{\rm{ }}m\)?

(b) Calculate the electric potential at this height.

(c) Sketch electric field and equipotential lines for this scenario.

Give the reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. What is the independent reason that a dielectric material also allows a greater voltage to be applied to a capacitor? (The dielectric thus increases \(C\) and permits a greater \(V\).

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