Igcse Model Questions Vol1 2024 Physics Question 4

A 12.0 V battery has an internal resistance of \(r = 0.50\ \Omega\). It supplies power to a resistive heating element whose resistance at \(20^{\circ}\text{C}\) is \(R_{20} = 8.0\ \Omega\). The element's temperature coefficient of resistance is \(\alpha = 4.0 \times 10^{-3}\ \text{°C}^{-1}\). The element is allowed to heat until its temperature reaches \(120^{\circ}\text{C}\). (a) Calculate the current drawn from the battery and the power dissipated in the element at \(20^{\circ}\text{C}\). (b) Determine the resistance of the element at \(120^{\circ}\text{C}\). (c) Calculate the current and the power dissipated in the element at \(120^{\circ}\text{C}\). (d) Find the overall efficiency (useful heating power divided by total power supplied by the battery) when the element is at \(120^{\circ}\text{C}\).