Physics PY1053 Homework Set 4 1. A 14 µF capacitor discharges through a 4 MΩ resistor. Find the time taken for the charge on the capacitor to decay to one tenth of its original value. 2. A 5 µF capacitor is connected in parallel with a 2 MΩ resistor and the combination is then connected in series with a 1 MΩ resistor through a switch to a 12 V battery. Find the time taken for voltage across the capacitor to rise from zero initial value to 2 V after the switch is closed. 3. A 4 Ω resistor is immersed in a thermally insulated calorimeter containing 0.1 kg of water. Assuming the calorimeter heat capacity is negligible, how long would it take to heat the water by 10 K if a current of 20 A is passing through the resistor? (The heat capacity of water is 4180 J/kg/K. Neglect heat losses from the calorimeter to its surroundings.) 4. (i) Write down equations, expressing Kirchoff’s rule for loop 1 and loop 2 in the circuit diagram on the left. (ii) Write the equations for the junction rule for junctions A and B. (iii) Solve the resulting set of simultaneous equations for the currents, I1, I2 and I3. 5. A 12 V battery of internal resistance 0.01 Ω is connected to a starting motor of resistance 0.1 Ω. (i) Find the current in the motor. (You may assume that the motor does not rotate.) (ii) What is the rate of heat generation in the coils of the motor? (iii) What is the rate of heat generation in the battery? 6. The terminals of a battery of internal resistance r are connected across a resistor R. For what value of R is the maximum power generated in the resistor R? 7. (i) In electron-­‐volts (eV), how much work does an ideal battery with a 15.0 V emf do on an electron that passes through the battery from the positive to the negative terminal? (ii) If 3 × 1019 electron pass through each second, what is the power of the battery in watts?