Question

Amy needs 5.0 V for some integrated circuit experiments. She uses a 9.0 V battery and two resistors to make a voltage divider. One resistor is 310 . She decides to make the other resistor smaller. What value should it have

Answer 1

Answer:

The value of smaller resistor is 248 Ω.

Explanation:

Voltage divider circuit is used to convert a higher voltage to a smaller voltage with the help of resistors which are connected in parallel.

As shown in the circuit, Vs is the source voltage, R₁ and R₂ are the two resistors and V₀ is the output voltage.

Applying KVL in the circuit, the output voltage is given by :

$V_{0} = \frac{V_{s}R_{2} }{R_{1} + R_{2} }$

According to the problem, R₂ = 310Ω , V₀ = 5 V and Vs = 9 V. Substitute these values in the above equation.

$5 = \frac{9\times310 }{R_{1} + 310 }$

$R_{1}+310 = \frac{9\times310}{5}$

$R_{1} = 558 - 310$

R₁ = 248Ω