Electric circuits with resistors in parallel and internal resistance – problems and solutions

1. Based on the figure below, if the source of electromotive force (emf) is 24 Volt, determine electric current I.

__Known :__

Source of emf = 24 Volt

Internal resistance (r) = 2 Ohm

Resistor 40 Ohm, 20 Ohm, and 20 Ohm.

__Wante__d : Electric current I

__Solution :__

Resistors connected in parallel, the equivalent resistor :

1/R = 1/40 + 1/20 + 1/20

1/R = 1/40 + 2/40 + 2/40

1/R = 5/40

R = 40/5

R = 8 Ohm

Terminal voltage :

V = emf – I r

V = 24 – I 2

Electric current I :

V = I R

24 – I 2 = I 8

24 = I 8 + I 2

24 = I (10)

I = 24/10

I = 2.4 Ampere

2. Based on figure below, if R_{1} = 3 Ω, R_{2} = 4 Ω, R_{3} = 4 Ω and electric current is 0.5 A. Determine electric voltage.

__Known :__

Electric current (I) = 0.5 Ampere

Resistor R_{1} = 3 Ohm

Resistor R_{2 }= 4 Ohm

Resistor R_{3} = 4 Ohm

__Wanted :__ Electric voltage (V)

__Solution :__

Calculate the equivalent resistance :

R_{2} and R_{3} are connected in parallel. The equivalent resistor :

1/R_{23} = 1/R_{2} + 1/R_{3 }= 1/4 + 1/4 = 2/4

R_{23 }= 4/2 = 2 Ohm

R_{1} and R_{23} are connected in series. The equivalent resistor :

R = R_{1} + R_{23} = 3 + 2 = 5 Ohm

Electric voltage :

V = I R = (0.5)(5) = 2.5 Volt