1. Capacitance. a. What is the physical description of a capacitor? b. What is t
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1. Capacitance. a. What is the physical description of a capacitor? b. What is the mathematical definition of capacitance? c. Based on the physical description of capacitance, why would you expect a plate to hold more excess charge on each of its conducting surfaces when the voltage difference between the two pieces of conductor increases? d. Explain why you expect to find that the amount of charge a battery can pump onto a parallel plate capacitor will double if the area of each plate doubles. e. Explain why you expect to find that the amount of charge a battery can pump onto a parallel plate capacitor will be cut in half (or at least reduced) if the distance between each plate doubles.Explanation / Answer
a)A capacitor is basically a device that stores electric charge. Its consists of plates separated by an insulator(air mostly). The plates have certain area and are separated by some distance.
b)Mathematically, the capacitance of a capacitor is given by:
C = e0 A/d
where e0 is a constant, A is the area of the plates ; d is the separation.
c)Q = CV
Charge is directly propotional to the Voltage across the plates.
So as voltage difference increases, the charge also increases.
d)We know that
C = e0 A/d
C' = e0 2A/d
C'/C = 2 => C' = 2C
Q = CV ; Q' = 2CV
Q'/Q = 2 => Q' = 2Q
the capacitance is directly proportional to the Area of the plates, so if the area is doubled, C also doubles and Q = CV, Charge is directly proportional to capacitance of the capacitor, as C is doubled, Q will also be doubled.
e)We know that
C = e0 A/d
C' = e0 A/2d = e0 A/2d
C'/C = 1/2 => C' = 1/2 C
Q = CV
Q' = 1/2 C V
Q'/Q = 1/2 => Q' = 1/2 Q
so we see that the charge is direcylt proportional to capacitance and capacitance is inversely proportional to the distance between the plates, if it doubles, C halves and hence the charge also gets halved.
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