Resistors circuits – problems and solutions

1. Which one of the resistors circuits, as shown in the figure below, has bigger resistance.

Answer A

R₁ = 2 Ω, R₂ = 2 Ω, R₃ = 6 Ω, R₄ = 6 Ω

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

1/R₃₄ = 1/R₃ + 1/R₄ = 1/6 + 1/6 = 2/6

R₃₄ = 6/2 = 3 Ω

R_1, R₂ and R₃₄ are connected in series. The equivalent resistor :

R = R₁ + R₂ + R₃₄ = 2 Ω + 2 Ω + 3 Ω

R = 7 Ω

Answer B

R₁ = 2 Ω, R₂ = 4 Ω, R₃ = 4 Ω, R₄ = 8 Ω

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

R₂₃ = R₂ + R₃ = 4 Ω + 4 Ω = 8 Ω

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

1/R₂₃₄ = 1/R₂₃ + 1/R₄ = 1/8 + 1/8 = 2/8

R₂₃₄ = 8/2 = 4 Ω

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

R = R₁ + R₂₃₄ = 2 Ω + 4 Ω

R = 6 Ω

Answer C

R₁ = 9 Ω, R₂ = 9 Ω, R₃ = 9 Ω, R₄ = 2 Ω

R_1, R₂ and R₃ are connected in parallel. The equivalent resistor :

1/R₁₂₃ = 1/R₁ + 1/R₂ + 1/R₃ = 1/9 + 1/9 + 1/9 = 3/9

R₁₂₃ = 9/3 = 3 Ω

R₁₂₃ and R₄ are connected in series. The equivalent resistor :

R = R₁₂₃ + R₄ = 3 Ω + 2 Ω

R = 5 Ω

Answer D

R₁ = 5 Ω, R₂ = 10 Ω, R₃ = 2 Ω, R₄ = 2 Ω

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

1/R₁₂ = 1/R₁ + 1/R₂ = 1/5 + 1/10 = 2/10 + 1/10

1/R₁₂ = 3/10

R₁₂ = 10/3 Ω

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

1/R₃₄ = 1/R₃ + 1/R₄ = 1/2 + 1/2 = 2/2

R₃₄ = 1 Ω

R₁₂ and R₃₄ are connected in series. The equivalent resistor :

R = R₁₂ + R₃₄ = 10/3 + 3/3 = 13/3

R = 4.3 Ω

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2. What is the equivalent resistor in the circuit as shown in figure below.

Solution :

Resistor 6 Ω, 3 Ω and 2 Ω are connected in parallel. The equivalent resistor :

1/R_P = 1/6 + 1/3 + 1/2 = 1/6 + 2/6 + 3/6 = 6/6

R_P = 6/6 = 1 Ω

Resistor 7 Ω, 8 Ω and 1 Ω are connected in series. The equivalent resistor :

R = 7 + 8 + 1 = 16 Ω

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3. What is the equivalent resistor in the circuit as shown in figure below.

Known :

Resistor 1 (R₁) = 2 Ohm

Resistor 2 (R₂) = 2 Ohm

Resistor 3 (R₃) = 2 Ohm

Resistor 4 (R₄) = 2 Ohm

Wanted : The equivalent resistor

Solution :

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

1/R₂₃ = 1/R₂ + 1/R₃

1/R₂₃ = 1/2 + 1/2 = 2/2

R₂₃ = 1 Ohm

Resistor R₁, resistor R₂₃ and resistor R₃ are connected in series. The equivalent resistor :

R = R₁ + R₂ + R₃ = 2 + 1 + 2

R = 5 Ohm