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A circuit contain two resistance $R_1$ and $R_2$ in series. Find the ratio of input voltage to voltage of $\mathrm{R}_2$.
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Verified Answer
The correct answer is:
$\frac{R_1+R_2}{R_2}$
The situation is shown in the circuit diagram.
Current flowing through the circuit,
$I=\frac{V_i}{R_1+R_2}$
Voltage across $R_2, V_2=R_2, V_2=\frac{V_i R_2}{R_1+R_2}$
$\Rightarrow \quad \frac{R_1+R_2}{R_2}=\frac{V_i}{V_2} \Rightarrow \frac{V_i}{V_2}=\frac{R_1+R_2}{R_2}$
Current flowing through the circuit,
$I=\frac{V_i}{R_1+R_2}$
Voltage across $R_2, V_2=R_2, V_2=\frac{V_i R_2}{R_1+R_2}$
$\Rightarrow \quad \frac{R_1+R_2}{R_2}=\frac{V_i}{V_2} \Rightarrow \frac{V_i}{V_2}=\frac{R_1+R_2}{R_2}$
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