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.

Wanted : 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

[irp]

2. Based on figure below, if R₁ = 3 Ω, R₂ = 4 Ω, R₃ = 4 Ω and electric current is 0.5 A. Determine electric voltage.

Known :

Electric current (I) = 0.5 Ampere

Resistor R₁ = 3 Ohm

Resistor R₂ = 4 Ohm

Resistor R₃ = 4 Ohm

Wanted : Electric voltage (V)

Solution :

Calculate the equivalent resistance :

R₂ and R₃ are connected in parallel. The equivalent resistor :

1/R₂₃ = 1/R₂ + 1/R₃ = 1/4 + 1/4 = 2/4

R₂₃ = 4/2 = 2 Ohm

R₁ and R₂₃ are connected in series. The equivalent resistor :

R = R₁ + R₂₃ = 3 + 2 = 5 Ohm

Electric voltage :

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

[irp]