# Resistors circuits – problems and solutions

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

R1, R2 and R34 are connected in series. The equivalent resistor :

R = R1 + R2 + R34 = 2 Ω + 2 Ω + 3 Ω

R = 7 Ω

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

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

R1, 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

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/RP = 1/6 + 1/3 + 1/2 = 1/6 + 2/6 + 3/6 = 6/6

RP = 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 