(a) Explain the statement the capacitance of a capacitor is 5\(\mu\)F. (b)(i) State the factors upon which the capacitance of a parallel plate capacitor depend. (ii) State how the capacitance depends on each of these factors stated in (b)(i). (c) A series arrangement of three capacitors of values 8uF, 12\(\mu\)F, and 24\(\mu\)F is connected in series with 90-V battery. (i) Draw an open-circuit diagram for this arrangement. (ii) Calculate the effective capacitance in the circuit. (iii) On closed circuit, calculate the charge on each capacitor when fully charged. (iv) Determine the p.d across the 8\(\mu\)F capacitor.
Explanation
(a) The statement means that an electric charge of 5\(\mu\)F is stored by the fully charged capacitor when connected to a d.c source of 1V. (b)(i)
(i) Factors
(ii) Form of dependence
- Common area of plates- Distance between plates- Permitivity or nature of dielectric
- Direct proportionality- Inverse proportionality- Direct proportionality
(c)(i)
(ii) \(\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_1} + \frac{1}{C_3}\) = \(\frac{1}{8} + \frac{1}{12} + \frac{1}{20} = \frac{3 + 2 + 1}{24}\) C = \(\frac{24}{6} = 4 \mu F\) (iii) Q = CV = 4 x 10\(^{-6}\) x 90 = 360\(\mu\)C charge on 8\(\mu\) FV = \(\frac{Q}{C} = \frac{360}{8}\) = 45V
