A circuit contain two resistance $R_1$ and $R_2$ in series. Find the ratio of input voltage to voltage of $\mathrm{R}_2$.

• A

  $\frac{R_2}{R_1+R_2}$
• Correct answer
  B

  $\frac{R_1+R_2}{R_2}$
• C

  $\frac{R_1+R_2}{R_1}$
• D

  $\frac{R_1}{R_1+R_2}$

Solution

The situation is shown in the circuit diagram. Current flowing through the circuit, $I=\frac{V_i}{R_1+R_2}$ Voltage across $R_2, V_2=R_2, V_2=\frac{V_i R_2}{R_1+R_2}$ $\Rightarrow \quad \frac{R_1+R_2}{R_2}=\frac{V_i}{V_2} \Rightarrow \frac{V_i}{V_2}=\frac{R_1+R_2}{R_2}$

Hence, the correct answer is option: 'B'.