Neco 2024 Physics Question 14

A battery of emf \(E = 12\ \text{V}\) has an internal resistance of \(0.5\ \Omega\). It is connected in series with an unknown resistor \(R\) and a parallel network consisting of a \(4\ \Omega\) resistor and another unknown resistor \(R_2\). The total current measured in the circuit is \(2.0\ \text{A}\). It is also known that the voltage across the parallel network is \(6.0\ \text{V}\) under this condition. (a) Determine the values of \(R\) and \(R_2\). (b) If the resistor \(R\) heats up and its resistance increases by 10 % while the battery emf and internal resistance remain unchanged, calculate the new total current flowing in the circuit. Give the current to two decimal places.