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Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD
as shown in the figure below. Calculate the equivalent resistance of the combination
between A and B?
as shown in the figure below. Calculate the equivalent resistance of the combination
between A and B?
Most Upvoted Answer
Four resistors each of resistance 2.0 Ω are joined end to end to form ...
Understanding the Configuration
In the given configuration, four resistors of 2.0 Ω each are connected in the form of a square ABCD. The objective is to find the equivalent resistance between points A and B.
Visualizing the Resistors
- Resistor R1 connects A to B (2.0 Ω)
- Resistor R2 connects B to C (2.0 Ω)
- Resistor R3 connects C to D (2.0 Ω)
- Resistor R4 connects D to A (2.0 Ω)
Identifying the Pathways
When calculating the equivalent resistance between points A and B, the two pathways available are:
- Directly through R1 (2.0 Ω)
- Indirectly through R2 and R4 (R2 in series with R4)
Calculating the Indirect Pathway
1. Resistance through R2 and R4:
- R2 + R4 = 2.0 Ω + 2.0 Ω = 4.0 Ω
Combining the Resistances
Now, you have two paths:
- Path 1: Direct connection through R1 = 2.0 Ω
- Path 2: Indirect connection = 4.0 Ω
These two paths are in parallel. The formula for two resistances in parallel (R1 and R2) is:
1 / Req = 1 / R1 + 1 / R2
Substituting the values:
1 / Req = 1 / 2.0 + 1 / 4.0
Simplifying the Equation
- 1 / Req = 0.5 + 0.25
- 1 / Req = 0.75
Thus,
Req = 1 / 0.75 = 1.33 Ω
Final Result
The equivalent resistance between points A and B in the square configuration is approximately 1.33 Ω.
In the given configuration, four resistors of 2.0 Ω each are connected in the form of a square ABCD. The objective is to find the equivalent resistance between points A and B.
Visualizing the Resistors
- Resistor R1 connects A to B (2.0 Ω)
- Resistor R2 connects B to C (2.0 Ω)
- Resistor R3 connects C to D (2.0 Ω)
- Resistor R4 connects D to A (2.0 Ω)
Identifying the Pathways
When calculating the equivalent resistance between points A and B, the two pathways available are:
- Directly through R1 (2.0 Ω)
- Indirectly through R2 and R4 (R2 in series with R4)
Calculating the Indirect Pathway
1. Resistance through R2 and R4:
- R2 + R4 = 2.0 Ω + 2.0 Ω = 4.0 Ω
Combining the Resistances
Now, you have two paths:
- Path 1: Direct connection through R1 = 2.0 Ω
- Path 2: Indirect connection = 4.0 Ω
These two paths are in parallel. The formula for two resistances in parallel (R1 and R2) is:
1 / Req = 1 / R1 + 1 / R2
Substituting the values:
1 / Req = 1 / 2.0 + 1 / 4.0
Simplifying the Equation
- 1 / Req = 0.5 + 0.25
- 1 / Req = 0.75
Thus,
Req = 1 / 0.75 = 1.33 Ω
Final Result
The equivalent resistance between points A and B in the square configuration is approximately 1.33 Ω.
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Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B?
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Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B?.
Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four resistors each of resistance 2.0 Ω are joined end to end to form a square ABCD as shown in the figure below. Calculate the equivalent resistance of the combination between A and B?.
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