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Lesson_3.1

# Lesson_3.1 - Lesson 3.1 Capacitance 1 Capacitance As a...

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Lesson 3.1 Capacitance 1. Capacitance As a conductor gets charged, its potential increases. The amount of charge given to a conductor to increase its potential by 1 volt is called the capacitance of the conductor. We use C to represent capacitance. Since capacitance is charge per unit volt, Q C V = Since Q is measured in coulombs and V is measured in volts, C is measured in coulombs per volt (C.V -1 ) and is called a farad (F). Since farad is a very large unit we very often use microfarad ( μ F = 10 -6 F), nanofarad (nF = 10 -9 F) and picofarad (pF = 10 -12 F) which are the submultiples of a farad. You have seen earlier that the potential of a spherical conductor which carries a charge Q is R Q R kQ V 0 4 πε = = Therefore, capacitance of a spherical conductor can be written as 0 0 4 / 4 Q Q C R V Q R πε πε = = = …1 Example 1 : An isolated spherical conductor of radius 10 cm is charged to 2.0 kV. (a) How much charge is on the conductor? (b) What is the capacitance of the sphere? (c) How does the capacitance change if the sphere is charged to 6.0 kV? Solution: (a) The capacitance of a spherical conductor C = 4 πε o R = 4 π × 8.85 × 10 -12 × 0.1 = 1.1 × 10 -11 F = 11 pF But V Q C = . Q = C V = 1.1 × 10 -11 × 2.0 × 10 3 = 2.2 × 10 -8 C = 22 nC

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(b) C = 11 pF (c) C does not depend on the amount of charge or the potential of the conductor, it only depends on the physical dimensions of the conductor. In order to raise the voltage to 6.0 kV, there is a proportional increase in the amount of charge on the conductor. Therefore, the ratio Q/V will remain the same. The capacitance is still 11 pF 2. Capacitor. + + + + + + + C=Q/V + + + + + + + - - - - - - - - - + + + + + + + + + (a) (b) Fig. 1 neutral conductor + + + + + + - - - - - - - - - grounded (c) Fig. 1(a) shows a conductor carrying a charge Q so that its potential is V volts. The capacitance of the conductor is given by V Q C = . Fig 1(b) shows a neutral conductor brought near the charged conductor. The negative charges in the neutral conductor move so that they reside closer to the positively charged conductor making the other end of the neutral conductor positive. The accumulation of negative charges near the positively charged object lowers its positive potential to V’ so that V’ < V. This decrease in potential of the charged conductor without changing the amount of charge on it causes an increase in its capacitance. In order to increase the potential back to V, more positive charges need to be given to the conductor. Thus the presence of a neutral conductor near the charged conductor raises the capacitance of the charged conductor. If now the neutral conductor is grounded, the positive
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Lesson_3.1 - Lesson 3.1 Capacitance 1 Capacitance As a...

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