Cambridge International AS and A level Physics
Exercise 12.2 Using the internal resistance equations This exercise will give you practice using, rearranging and performing calculations involving internal resistance. You will use equations such as V = IR but must choose the right voltage and resistance. 1 The e.m.f. of a battery is 9.0 V. When a resistor is connected to the battery, the voltmeter reading drops to 8.0 V and the current is 0.40 A. a Calculate the resistance of the external resistor. b Calculate the internal resistance of the battery. 2 A 9.0 Ω resistor is connected to a battery of e.m.f. 4.0 V and internal resistance 1.0 Ω. a Calculate the current in the circuit. (Only the e.m.f. is given, so choose as R the total resistance of the circuit.) b Calculate the p.d. across the 9.0 Ω resistor. c State the p.d. across the battery terminals. d State the p.d. across the battery terminal when the resistor is removed. (Without any resistor, the battery is said to be in an open circuit.) 3 A battery of e.m.f. 6.0 V is connected across a 10 Ω resistor. The p.d. across the resistor is 4.0 V. a Calculate the current in the circuit. (You cannot use the e.m.f. directly in V = IR because you do not know the total resistance.) b Calculate the internal resistance of the battery. 4 This graph shows the variation of the potential difference across a cell with the current in it: 1.50
1.00 P.d. / V
68
0.50
0
0
0.5
1.0
1.5 Current / A
2.0
2.5
3.0
a Rearrange the formula E = V + Ir to find expressions for the gradient of the graph and for the y-intercept of the graph in terms of E and r. b Use the graph to find the internal resistance of the cell. c Draw a circuit diagram of all the apparatus needed to be able to take the measurements shown in the graph. Your apparatus should enable the current to be adjusted. 5 A torch is powered by a 4.5 V battery. The p.d. across the filament lamp in the torch is 3.8 V and the power produced in the lamp is 0.80 W. a Calculate the current in the lamp. (There are many equations to choose from, but without knowing a resistance you must use an equation for power.) b Calculate the internal resistance of the battery. c Calculate the energy lost per second as heat in the internal resistance of the battery.