PY1006 Study Problems – Week 3 Capacitance, Current, Resistance (1) (a) Find the equivalent capacitance of the combination of capacitors shown above if C1 = 10.0 µF, C2 = 5.00 µF and C3 = 4.00 µF. Find the (b) charge, (c) potential difference and (d) stored energy for each capacity if V = 100 V. Hint: Capacitors C1 and C2 are in parallel, and the equivalent capacitor C12 is in series with C3 . Answers: (a) 3.16 µF; (b) Q1 = 2.11×10−4 C, Q2 = 1.05×10−4 C, Q3 = 3.16×10−4 C; (c) V1 = V2 = 21 V, V3 = 79 V; (d) U1 = 0.0022 J, U2 = 0.0011 J, U3 = 0.012 J (2) A fuse in an electric circuit is formed by a wire designed to melt (and thus open the circuit) if the current exceeds a specified value. The material making up the fuse melts when the current density reaches 440 A/cm2 . What diameter of cylindrical wire should be used for a fuse intended to limit the current to 0.50 A? Answer: (a) 0.38 mm (3) An electric cable is made up of 125 strands of fine wire, each having a resistance of 2.65µΩ. When a potential difference V is applied across the cable, the total current flowing is 0.750 A. (a) What is the current in each strand of wire? (b) What is the applied potential difference? (c) What is the total resistance of the cable? Answers: (a) 0.0060 A; (b) 1.59 × 10−8 V; (c) 2.12 × 10−8 Ω (4) A 230 V potential difference is applied to a space heater with a resistance of 14 Ω. (a) At what rate is electric energy transferred to heat energy? (b) If the cost of electricity is 16 cents per kW·hour, how much does it cost to operate the heater for 5.0 hours? Answers: (a) 3.78 kW; (b) EUR 3.02

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