Week 3 Capacitance, Current, Resistance

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