Question

A 10 V battery is connected to a voltage divider circuit

which consists of a 100 Ω resistor and a 300 Ω resistor.
a What is the voltage across the 300 Ω resistor?
A 2.5 V
B 3.3 V
C 7.5 V
D 13.3 V

b) What is the voltage drop across the 100 Ω resistor?
A 2.5 V
B 3.3 V
C 7.5 V
D 13.3 V

Answer 1

a) C. 7.5 V

b) A. 2.5 V

Step-by-step 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)(V)/(R)\\\\V_(2) = (300\ \Omega)(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