Question

A 10 V battery is connected to a voltage divider circuit

Answer 1

Answer:

a) C. 7.5 V

b) A. 2.5 V

Explanation:

First, we find the total resistance of the circuit. A voltage divider circuit is a series circuit. Therefore, its total resistance will be the sum of individual resistances:

$R = R_{1}+R_{2}\\R = 100\ \Omega + 300\ \Omega\\R = 400\ \Omega$

a)

Now, we will apply the voltage divider rule on this circuit to find the voltage across the 300 Ω Resistor (R₂):

$V_{2} = R_{2}\frac{V}{R}\\\\V_{2} = (300\ \Omega)\frac{10\ V}{400\ \Omega}$

V₂ = 7.5 V

Therefore, the correct option is:

C. 7.5 V

b)

Now, the voltage across the 100 Ω Resistor (R₁) will be:

$V = V_{1}+V_{2}\\V_{1} = V-V_{2}\\V_{1} = 10\ V - 7.5\ V\\V_{1}=2.5\ V$

Therefore,the correct option is:

A. 2.5 V