Simple DC circuits – problems and solutions

1. Based on the figure below, determine the electric current through R₁.

Known :

Resistor 1 (R₁) = 4 Ω

Resistor 2 (R₂) = 4 Ω

Resistor 3 (R₃) = 8 Ω

Electric voltage (V) = 40 Volt

Wanted: Electric current through R₁

Solution :

The electric current flows from high potential to low potential. The direction of electric current in the circuit above is the same as a clockwise direction.

The electric current that flows out of the battery

First, calculate the equivalent resistance (R). Thereafter, calculate the electric current using the equation of Ohm’s law :

V = I R or I = V / R

V = voltage, I = electric current, R = the equivalent resistance

The equivalent resistance :

Resistor R₁ and resistor R₂ are connected in parallel. The equivalent resistance :

1/R₁₂ = 1/R₁ + 1/R₂ = 1/4 + 1/4 = 2/4

R₁₂ = 4/2 = 2 Ω

Resistor R₁₂ and resistor R₃ are connected in series. The equivalent resistance :

R = R₁₂ + R₃ = 2 + 8 = 10 Ω

The electric current that flows out of the battery :

I = V / R = 40 / 10 = 4 A

The electric current that flows out of the battery is 4 Ampere.

Electric voltage V_ab and V_bc

Kirchhoff‘s first rule states that at any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction.

Based on Kirchhoff’s first rule, concluded that if the electric current flows out of the battery is 4 A then the electric current through a-b is equal to 4 Ampere, so also the electric current through b-c is 4 Ampere.

Electric voltage V_ab :

V_ab = I_ab R_ab = (4)(2) = 8 Volt

Electric voltage V_bc :

V_bc = I_bc R_bc = (4)(8) = 32 Volt

The above circuit is connected in series so that the total electrical voltage is V = V_ab + V_bc = 8 Volt + 32 Volt = 40 Volt.

The electric current flows through R₁ = 4 Ω

I₁ = V_ab / R₁ = 8 Volt / 4 Ohm = 2 A

I₂ = V_ab / R₂ = 8 Volt / 4 Ohm = 2 A

The electric current that flows out of the battery is 4 A. When it arrives at point a the electric current is divided into two, the electric current of 2 Ampere flows through the resistor R₁ and

the electric current of 2 A flows through the resistor R₂. 2 A + 2 A = 4 A.

2. Based on the figure below, determine the electric current that flows through resistor 4-Ω.

Known :

Resistor 1 (R₁) = 6 Ω

Resistor 2 (R₂) = 4 Ω

Resistor 3 (R₃) = 1.6 Ω

The electric voltage (V) = 16 Volt

Wanted: The electric current flows through 4 Ω

Solution :

The electric current flows from high potential to low potential. The direction of electric current in the circuit above is the same as a clockwise direction.

The electric current that flows out of the battery

The equivalent resistance :

Resistor R₁ and resistor R₂ are connected in parallel. The equivalent resistor :

1/R₁₂ = 1/R₁ + 1/R₂ = 1/6 + 1/4 = 2/12 + 3/12 = 5/12

R₁₂ = 12/5 = 2.4 Ω

Resistor R₁₂ and resistor R₃ are connected in series. The equivalent resistor :

R = R₁₂ + R₃ = 2.4 + 1.6 = 4 Ω

The electric current that flows out of the battery :

I = V / R = 16 / 4 = 4 A

The electric voltage V_ab and V_bc

Based on Kirchhoff’s first rule, concluded that if the electric current flows out of the battery is 4 A then the electric current through a-b is equal to 4 Ampere, so also the electric current through b-c is 4 Ampere.

The electric voltage V_ab :

V_ab = I_ab R_ab = (4)(2.4) = 9.6 Volt

The electric voltage V_bc :

V_bc = I_bc R_bc = (4)(1.6) = 6.4 Volt

The above circuit is connected in series so that the total electric voltage is V = V_ab + V_bc = 9.6 Volt + 6.4 Volt = 16 Volt.

The electric current that flows through R₂ = 4 Ω

I₁ = V_ab / R₁ = 9.6 Volt / 6 Ohm = 1.6 A

I₂ = V_ab / R₂ = 9.6 Volt / 4 Ohm = 2.4 A

The electric current that flows out of the battery is 4 A. When it arrives at point a the electric current is divided into two,

the electric current 1.6 A flows through the resistor R₁ and the electric current 2.4 A flows through the resistor R₂. 1.6 A + 2.4 A = 4 A.