Neco 2019 Physics Question 41

During a resistance measurement a 12.0\,V battery of unknown internal resistance \(r\) is connected in series with an ideal ammeter and an unknown resistor \(R\). A voltmeter of internal resistance \(R_v = 10\ \text{M}\Omega\) is placed across \(R\). The ammeter reading is 2.00\,mA and the voltmeter reading is 11.8\,V.\n\n(a) Determine the true resistance \(R\) and the internal resistance \(r\) of the battery.\n\n(b) If the voltmeter were replaced by one whose internal resistance is \(1\ \text{M}\Omega\), what would be the voltmeter reading (assuming the same \(R\) and \(r\))?\n\n(c) Calculate the percentage error made when \(R\) is estimated simply as \(V/I\) (ignoring \(r\)).\n\nState which change in the measuring instruments would most effectively reduce this percentage error.