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Chapter 26: Problem 1

(a) How much charge is on each plate of a \(4.00-\mu \mathrm{F}\) capacitor when it is connected to a \(12.0-\mathrm{V}\) battery? (b) If this same capacitor is connected to a \(1.50-\mathrm{V}\) battery, what charge is stored?

Short Answer

Expert verified
The charge on the capacitor when connected to a 12.0-Volt battery is \(4.8 \times 10^{-5} C\). When the same capacitor is connected to a 1.50-Volt battery, the charge is \(6 \times 10^{-6} C\).

Step by step solution

01

Calculating the charge for the 12.0-Volt battery

To find the charge when the capacitor is connected to a 12.0-Volt battery, we substitute the values into the formula \(Q = CV\) . The capacitance (C) is \(4.00碌F = 4.00 \times 10^{-6} F\) (1 碌F = \( 10^{-6} F\) ) and the voltage (V) = 12.0 V. Hence, Q = \(4.00 \times 10^{-6} F \times 12.0 V\).
02

Repeat step one for the 1.50-Volt battery

To find the charge when connected to a 1.50-Volt battery, we apply the formula as we did in step one, only this time substituting 1.50 V for the voltage. Hence, Q = \(4.00 \times 10^{-6} F \times 1.50 V\).

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Most popular questions from this chapter

An isolated capacitor of unknown capacitance has been charged to a potential difference of \(100 \mathrm{V}\). When the charged capacitor is then connected in parallel to an uncharged \(10.0-\mu \mathrm{F}\) capacitor, the potential difference across the combination is \(30.0 \mathrm{V}\). Calculate the unknown capacitance.

(a) Two spheres have radii \(a\) and \(b\) and their centers are a distance \(d\) apart. Show that the capacitance of this system is $$C=\frac{4 \pi \epsilon_{0}}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$$ provided that \(d\) is large compared with \(a\) and \(b\). (Suggestion: Because the spheres are far apart, assume that the potential of each equals the sum of the potentials due to each sphere, and when calculating those potentials assume that \(V=k_{e} Q / r\) applies.) \((\mathrm{b})\) Show that as \(d\) approaches infinity the above result reduces to that of two spherical capacitors in series.

Find the capacitance of the Earth. (Suggestion: The outer conductor of the "spherical capacitor" may be considered as a conducting sphere at infinity where \(V\) approaches zero.)

Two conductors having net charges of \(+10.0 \mu \mathrm{C}\) and \(-10.0 \mu \mathrm{C}\) have a potential difference of \(10.0 \mathrm{V}\) between them. (a) Determine the capacitance of the system. (b) What is the potential difference between the two conductors if the charges on each are increased to \(+100 \mu \mathrm{C}\) and \(-100 \mu \mathrm{C} ?\)

An isolated charged conducting sphere of radius \(12.0 \mathrm{cm}\) creates an electric field of \(4.90 \times 10^{4} \mathrm{N} / \mathrm{C}\) at a distance \(21.0 \mathrm{cm}\) from its center. (a) What is its surface charge density? (b) What is its capacitance?
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