Q$.$III$\mathrm{.}1.(10$ pts$)$ Multimeters are an essential electronics test and measurement tool, having a variety of functions, including the ability to measure voltage and current within a circuit. When measuring voltage, multimeters have a very high input resistance of several MS$.$ Let's assume the input resistance of a given multimeter is $10M$ for the purposes of this question. Assume you are measuring the voltage across R$2$ in the following circuit.

When you place your multimeter in parallel with R$2$ to measure the voltage drop across it$,$ the equivalent circuit model becomes the following, with $R_{\text{m}\text{e}\text{t}\text{e}\text{r}}$ representing the input resistance of the multimeter.

Please calculate the voltage drop across $R2$ without $R_{\text{m}\text{e}\text{t}\text{e}\text{r}}$ present, with $R_{\text{m}\text{e}\text{t}\text{e}\text{r}}=10M,$ and with $R_{\text{m}\text{e}\text{t}\text{e}\text{r}}=1k.$ Then use this information to explain why it is essential for multimeters to have a high input resistance when measuring voltage.

Voltage drop across R$2($without $R_{\text{m}\text{e}\text{t}\text{e}\text{r}})=(3$ pts$)$

Voltage drop across when $($:$R_{\text{m}\text{e}\text{t}\text{e}\text{r}}=10M$