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
R1, 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
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
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/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
[irp]
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