Neco Model Questions Vol1 2024 Physics Question 4

A battery of unknown emf E and internal resistance r is connected to a circuit as shown in the diagram. The circuit contains a switch S, an ammeter A placed in series with the battery, a voltmeter V connected across resistor R1, and two external resistors R1 = 4 Ω and R2 = 6 Ω that are placed in parallel when the switch is closed. When the switch S is closed the ammeter reads a total current I_total = 4.00 A and the voltmeter reads a voltage V_R1 = 9.60 V. When the switch is open (so that only R1 remains in the circuit) the ammeter reads I_R1_only = 2.50 A. Using the information above, answer the following: a) Determine the current through each external resistor (I_R1 and I_R2) when the switch is closed. b) Calculate the internal resistance r of the battery and its emf E. c) Compute: i) the total power supplied by the battery, ii) the power dissipated in each external resistor, iii) the power loss in the internal resistance, and iv) the efficiency of the circuit (percentage of the total power that is useful). d) A third resistor R3 = 12 Ω is now added in parallel with R1 and R2 (the switch remains closed). Determine the new total current drawn from the battery and the new terminal voltage across the parallel combination. Comment briefly on how the addition of R3 influences the efficiency of the circuit.