Electric circuits – problems and solutions

1. R₁, = 6 Ω, R₂ = R₃ = 2 Ω, and voltage = 14 volt, determine the electric current in circuit as shown in figure below.

Known :

Resistor 1 (R₁) = 6 Ω

Resistor 2 (R₂) = 2 Ω

Resistor 3 (R₃) = 2 Ω

Voltage (V) = 14 Volt

Wanted : Electric current (I)

Solution :

Equivalent resistor (R) :

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

1/R₂₃ = 1/R₂ + 1/R₃ = 1/2 + 1/2 = 2/2

R₂₃ = 2/2 = 1 Ω

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

R = R₁ + R₂₃ = 6 Ω + 1 Ω

R = 7 Ω

Electric current (I) :

I = V / R = 14 / 7 = 2 Ampere

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2. Which one of the electric circuits as shown below has the bigger current.

Solution :

The resistance of the resistor is R and the electric voltage is V.

Answer A.

R₁, R₂ and R₃ are connected in series. The equivalent resistor :

R_A = R₁ + R₂ + R₃ = R + R + R = 3R

Electric current (I) :

Answer B.

R₁, R₂ and R₃ are connected in parallel. The equivalent resistor :

1/R = 1/R₁ + 1/R₂ + 1/R₃ = 1/R + 1/R + 1/R = 3/R

R_B = R/3

Electric current (I) :

Answer C.

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

1/R₂₃ = 1/R₂ + 1/R₃ = 1/R + 1/R = 2/R

R₂₃ = R/2

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

R_C = R₁ + R₂₃ = R + R/2 = 2R/2 + R/2 = 3R/2

Electric current (I) :

Answer D.

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

1/R₁₂ = 1/R₁ + 1/R₂ = 1/R + 1/R = 2/R

R₁₂ = R/2

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

R_D = R₁₂ + R₃ = R/2 + R = R/2 + 2R/2 = 3R/2

Electric current (I) :

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3. R₁ = 4 ohm, R₂ = 6 ohm, R₃ = 2 ohm, and V = 24 volt. What is the electric current in circuit as shown in figure below.

Known :

Resistor 1 (R₁) = 4 Ohm

Resistor 2 (R₂) = 6 Ohm

Resistor 3 (R₃) = 2 Ohm

Voltage (V) = 24 Volt

Wanted : Electric current in circuit

Solution :

R₁, R₂ and R₃ are connected in series. The equivalent resistor :

R = R₁ + R₂ + R₃ = 4 + 6 + 2

R = 12 Ohm

Electric current :

I = V / R = 24 / 12 = 2 Ampere

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4. Which one of the electric circuits as shown below has the bigger current.

Solution

Electric current in circuit A.

The equivalent resistor :

R₁ = 3 Ω, R₂ = 4 Ω, R₃ = 4 Ω, V = 12 Volt

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

1/R₂₃ = 1/R₂ + 1/R₃ = 1/4 + 1/4 = 2/4 = 1/2

R₂₃ = 2/1 = 2 Ω

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

R = R₁ + R₂₃ = 3 Ω + 2 Ω = 5 Ω

Electric current (I) :

I = V / R = 12 / 5 = 2.4 Ampere

Electric current in circuit B.

The equivalent resistor :

R₁ = 8 Ω, R₂ = 2 Ω, R₃ = 2 Ω, V = 36 Volt

R₁, R₂ and R₃ are connected in series. The equivalent resistor :

R = R₁ + R₂ + R₃ = 8 + 2 + 2 = 12 Ω

Electric current (I) :

I = V / R = 36 / 12 = 3 Ampere

Electric current in circuit C.

The equivalent resistor :

R₁ = 4 Ω, R₂ = 4 Ω, R₃ = 6 Ω, V = 12 Volt

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

1/R₂₃ = 1/R₂ + 1/R₃ = 1/4 + 1/4 + 1/6 = 3/12 + 3/12 + 2/12 = 8/12

R₂₃ = 12/8 = 1.5 Ω

Electric current (I) :

I = V / R = 12 / 1.5 = 8 Ampere

Electric current in circuit D.

The equivalent resistor :

R₁ = 3 Ω, R₂ = 3 Ω, R₃ = 3 Ω, R₄ = 3 Ω, R₅ = 6 Ω, V = 24 Volt

R₂, R₃ and R₄ are connected in parallel. The equivalent resistor :

1/R₂₃₄ = 1/R₂ + 1/R₃ + 1/R₄ = 1/3 + 1/3 + 1/3 = 3/3

R₂₃₄ = 3/3 = 1 Ω

R₁, R₂₃₄ and R₅ are connected in series The equivalent resistor :

R = R₁ + R₂₃₄ + R₅ = 3 + 1 + 6 = 9 Ω

Electric current (I) :

I = V / R = 24 / 9 = 2.6 Ampere

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5. According to figure as shown below, determine :

A. Total resistance

B. Electric current in circuit

C. Current I₁

D. Current I₂

Known :

Resistor 1 (R₁) = 4 Ω

Resistor 2 (R₂) = 4 Ω

Resistor 3 (R₃) = 2 Ω

Resistor 4 (R₄) = 3 Ω

Electric voltage (V) = 12 Volt

Solution :

A. Total resistance (R)

Resistor R₂ and resistor R₃ are connected in series. The equivalent resistor :

R₂₃ = R₂ + R₃ = 4 Ω + 2 Ω = 6 Ω

Resistor R₂₃ and resistor R₄ are connected in parallel. The equivalent resistor :

1/R₂₃₄ = 1/R₂₃ + 1/R₄ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6

R₂₃₄ = 6/3 = 2 Ω

Resistor R₁ and resistor R₂₃₄ are connected series. The equivalent resistor :

R = R₁ + R₂₃₄ = 4 Ω + 2 Ω = 6 Ω

The total resistance is 6 Ohm.

B. Electric current in circuit (I)

V = I R

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

Electric current :

I = V / R = 12 Volt / 6 Ohm = 2 Ampere

C. Electric current I₁

Electric current in resistor R₁ = electric current in circuit = 2 Ampere.

D. Current I₂

Resistor R₂₃ and resistor R₄ are connected in parallel. The equivalent resistor R₂₃₄ = 2 Ohm.

Electric current in resistor R₂₃₄ = electric current in resistor R₁ = 2 Ampere.

Voltage in resistor R₂₃₄ is:

V = I R₂₃₄ = (2 A)(2 Ohm) = 4 Volt

Voltage in resistor R₂₃₄ = voltage in resistor R₄ = voltage in resistor R₂₃ = 4 Volt.

The equivalent resistor R₂₃ is 6 Ohm.

Electric current in resistor R₂₃ is :

I = V / R = 4 Volt / 6 Ohm = 2/3 Ampere

Electric current in resistor R₂₃ = Electric current in resistor R₂ = electric current in resistor R₃ = 2/3 Ampere.

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6. R₁ = R₂ = 10 Ω and R₃ = R₄ = 8 Ω. What is the electric current in circuit as shown in figure below ?

Known :

Resistor R₁ = Resistor R₂ = 10 Ω

Resistor R₃ = Resistor R₄ = 8 Ω

Electric voltage (V) = 12 Volt

Wanted : electric current (I)

Solution :

The equivalent resistor

Resistor R₃ and resistor R₄ are connected in parallel, the equivalent resistor :

1/R₃₄ = 1/R₃ + 1/R₄ = 1/8 + 1/8 = 2/8

R₃₄ = 8/2 = 4 Ω

Resistor R₁, R₂ and R₃₄ are connected in series, the equivalent resistor :

R = R₁ + R₂ + R₃₄ = 10 Ω + 10 Ω + 4 Ω = 24 Ω

Electric current :

I = V / R = 12 Volt / 24 Ohm = 0,5 Volt/Ohm = 0.5 Ampere

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7. If the internal resistance of battery ignored, what is the electric current in the circuit shown in figure below.

Known :

Resistor R₁ = 3 Ohm

Resistor R₂ = 3 Ohm

Resistor R₃ = 6 Ohm

Electric voltage (V) = 6 Volt

Wanted : Electric current (I)

Solution :

Equivalent resistor

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

R₁₂ = R₁ + R₂ = 3 Ohm + 3 Ohm = 6 Ohm

Resistor R₁₂ and resistor 3 are connected in parallel. The equivalent resistor :

1/R = 1/R₁₂ + 1/R₃ = 1/6 + 1/6 = 2/6

R = 6/2 = 3 Ohm

Electric current :

I = V / R = 6 / 3 = 2 Ampere

8. What is the total electric current in circuit as shown in figure below.

Known :

Resistor R₁ = 6 Ohm

Resistor R₂ = 4 Ohm

Electric current (V) = 6 Volt

Internal resistance (r) = 0.6 Ohm

Wanted : Electric current

Solution :

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

1/R_P = 1/R₁ + 1/R₂ = 1/6 + 1/4 = 4/24 + 6/24 = 10/24

R_P = 24/10 = 2.4 Ohm

Resistor R_P and internal resistance (r) are connected in series. The equivalent resistor :

R = R_P + r = 2.4 Ohm + 0.6 Ohm = 3.0 Ohm

Electric current in circuit :

I = V / R = 6 Volt / 3 Ohm = 2 Ampere