Sheet 5 1. What is the charge stored when the voltage across a 50 μF capacitor is 9 V? Q = VC = 9 V × 50 μF = 450 μF 2. What is the capacitance of a capacitor that stores 12 μC of charge when connected to a 6 V battery? C = Q 12 μC = = 2 μC V 6V 3. Work out the voltage across the plates of a 10 μF capacitor when it has a charge of 50 μC. V = Q 50 μC = = 5V C 10 μF 4. Calculate the energy stored in a capacitor with a charge of 200 μC and 9 V across its plates. W = ½ QV = 200 μC × 9 V = 0.9 mJ 2 5. Calculate the energy stored in a 1 μF capacitor charged to 50 V. W = ½ V 2C = 2500 V × 1 mF = 1.25 mJ 2 6. What is the combined capacitance of: a) a 2.2 μF capacitor and a 4.7 μF capacitor in parallel? CTOTAL = C1 + C2 = 2.2 μF + 4.7 μF = 6.9 μF b) two 100 μF capacitors in series? CTOTAL = C1 × C2 10,000 μF = = 50 μF C1 + C2 200 μF 7. What is the total combined capacitance of the network shown below? CTOTAL = C1 × (C2 + C3) 5 μF × 25 μF = = 4.167 μF C1 + (C2 + C3) 30 μF 8. A parallel plate air capacitor is made by using two metallic 16 cm2 plates 4.7 mm apart. It is connected to a 12-V battery. (a) What is the capacitance? (b) What is the charge on each plate, (c) What is the energy stored in the capacitor? (d) If the battery is disconnected and the plates are pulled apart to a separation of 9.4 mm, what are the answers to (a), (b) and (c)? c) d) c) 9. 10. Calculate the equivalent capacitor Since above three highlighted capacitors are in series, so their equivalent capacitance (Cx) will be: 1/Cx = 1/3 + 1/3 +1/3 1/Cx = 3/3 = 1 Cx = 1μf After substituting the 1μf instead of three series capacitors, we can see that now 1μf and 2μf are in parallel, so their equivalent (Cy) will be: Cy = 1 + 2 Cy = 3μf Now after further simplification, again three 3μf capacitors are in series, So their equivalent(Cz) will be: 1/Cz = 1/3 + 1/3 +1/3 1/Cz = 3/3 = 1 Cz = 1μf Again combination of series capacitors (1μf) and 2μf are in parallel, so their equivalent(Ct) will be: Ct = 1 + 2 Ct =3μf Now finally three capacitors are series so their equivalent will be: 1/C = 1/3 + 1/3 +1/3 1/C = 3/3 = 1 C = 1μf