Question

A circuit contain two resistors R₁ and R₂ in series. Find the ratio of input voltage to voltage to R₂ 

• A. $\frac{R_{2}}{R_{1}+R_{2}}$
• B. $\frac{R_{1}+R_{2}}{R_{2}}$
• C. $\frac{R_{1}+R_{2}}{R_{1}}$
• D. $\frac{R_{1}}{R_{1}+R_{2}}$

Answer 1

The Correct Option is B

In a series circuit, the same current flows through both resistors, but the voltage is divided between them. The total voltage across the circuit is equal to the sum of the voltage across each resistor.

Let Vin be the input voltage, V1 be the voltage across R₁ and V₂ be the voltage across R₂.

Then, we have:

\(Vin = V_1 + V_2 ...(1)\)

Also, since R1 and R2 are in series, the current through them is the same. Let I be the current flowing through the circuit.

Then, by Ohm's law:

\(V_1 = I * R_1....(2)\)

\(V_2 = I * R_2....(3)\)

Dividing equations (2) and (3), we get:

\(\frac{V_2}{V_1} = \frac{R_2}{R_1}\)

Substituting equation (1) into (2), we get:

\(V_1 = Vin - V_2\)

Substituting equation (3) into the above equation, we get:

\(V_1 = Vin - (I * R2)\)

Substituting equation (2) into the above equation, we get:

\(V_1 = Vin - (V2 * \frac{R_1}{R_2})\)

Multiplying both sides by R2, we get:

\(V_1 * R_2 = Vin * R_2 - V_2 * R_1\)

Dividing both sides by V2, we get:

\(\frac{V_1}{V_2} = \frac{Vin }{V_2} - \frac{R_1}{R_2}\)

So, the ratio of input voltage to voltage across R2 is:

\(\frac{Vin}{V_2 }= \frac{V_1}{V_2}+ \frac{R_1}{R_2} = \frac{(R_1 + R_2) }{ R_2}\)

Therefore, the correct option is(B):  \(\frac{(R_1 + R_2) }{R_2}\).