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Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will be
- a)32
- b)64
- c)50
- d)200
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Three resistors are connected to form the sides of a triangle ABC, the...
Here resistor of side BC & AC are in series so
equ resis.= 100+60
= 160Ω
now this resis.is in parallel with resistance of AB
so1/rₑ= (1/40)+(1/160)
equ.resistance = 32
equ resis.= 100+60
= 160Ω
now this resis.is in parallel with resistance of AB
so1/rₑ= (1/40)+(1/160)
equ.resistance = 32
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Three resistors are connected to form the sides of a triangle ABC, the...
Solution:
To find the effective resistance between points A and B, we need to find the equivalent resistance of the two resistors connected in parallel. Let's call this equivalent resistance R1.
Step 1: Find the equivalent resistance of BC and CA.
Since BC and CA are connected in series, we can find their equivalent resistance (R2) using the formula:
R2 = BC + CA = 60 + 100 = 160 ohms
Step 2: Find the equivalent resistance of AB and R2.
Since AB and R2 are connected in parallel, we can find their equivalent resistance (R1) using the formula:
1/R1 = 1/AB + 1/R2
R1 = AB * R2 / (AB + R2)
Substituting the values of AB and R2, we get:
R1 = 40 * 160 / (40 + 160) = 32 ohms
Therefore, the effective resistance between points A and B is 32 ohms, which is option A.
To find the effective resistance between points A and B, we need to find the equivalent resistance of the two resistors connected in parallel. Let's call this equivalent resistance R1.
Step 1: Find the equivalent resistance of BC and CA.
Since BC and CA are connected in series, we can find their equivalent resistance (R2) using the formula:
R2 = BC + CA = 60 + 100 = 160 ohms
Step 2: Find the equivalent resistance of AB and R2.
Since AB and R2 are connected in parallel, we can find their equivalent resistance (R1) using the formula:
1/R1 = 1/AB + 1/R2
R1 = AB * R2 / (AB + R2)
Substituting the values of AB and R2, we get:
R1 = 40 * 160 / (40 + 160) = 32 ohms
Therefore, the effective resistance between points A and B is 32 ohms, which is option A.
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Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will bea)32b)64c)50d)200Correct answer is option 'A'. Can you explain this answer?
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