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Four resistances 10Ω, 5Ω, 7Ω and 3Ω are connected, so that they form the sides of a rectangle AB, BC, CD and DA, respectively. Another resistance of 10Ω is connected across the diagonal AC. The equivalent resistance between A and B is
- a)2Ω
- b)5Ω
- c)7Ω
- d)10Ω
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Four resistances 10Ω, 5Ω, 7Ω and 3Ω are connected, so that they form ...
3Ω resistor and 7Ω resistor are in series.
Therefore, resultant = 10Ω (7 + 3)
This 10Ω equivalent resistance is in parallel with resistance (10Ω) in arm AC.
⇒ R1 = 5Ω
Again R2 is in parallel with resistance (10Ω) in arm AB.
⇒ R = 5Ω
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Community Answer
Four resistances 10Ω, 5Ω, 7Ω and 3Ω are connected, so that they form ...
Explanation:
To find the equivalent resistance between points A and B, we can use the concept of series and parallel combinations of resistances.
Step 1: Identifying the resistances and their connections
We have four resistances: 10Ω, 5Ω, 7Ω, and 3Ω. They are connected in the shape of a rectangle, with resistances 10Ω and 5Ω forming one side, and resistances 7Ω and 3Ω forming the other side. Another resistance of 10Ω is connected across the diagonal AC.
Step 2: Simplifying the circuit
We can simplify the circuit by reducing the resistances that are in series or parallel. Let's start with the resistances in series.
The resistances 10Ω and 5Ω are in series, so their equivalent resistance is:
R1 = 10Ω + 5Ω = 15Ω
Similarly, the resistances 7Ω and 3Ω are in series, so their equivalent resistance is:
R2 = 7Ω + 3Ω = 10Ω
Now, let's consider the resistance across the diagonal AC. This resistance is in parallel with the resistor R1.
Step 3: Calculating the equivalent resistance
To find the equivalent resistance between points A and B, we need to calculate the total resistance when resistors R2 and the parallel combination of R1 and the diagonal resistance are in series.
The equivalent resistance of the parallel combination of R1 and the diagonal resistance (RD) can be calculated using the formula:
1/RT = 1/R1 + 1/RD
Substituting the values:
1/RT = 1/15Ω + 1/10Ω
Simplifying this expression:
1/RT = (2 + 3)/30Ω
1/RT = 5/30Ω
1/RT = 1/6Ω
Therefore, the equivalent resistance between points A and B is 6Ω.
Step 4: Checking the options
The correct answer is given as 5Ω, which doesn't match the calculated equivalent resistance of 6Ω. Therefore, there might be an error in the given answer options, or the calculations might need to be rechecked.
To find the equivalent resistance between points A and B, we can use the concept of series and parallel combinations of resistances.
Step 1: Identifying the resistances and their connections
We have four resistances: 10Ω, 5Ω, 7Ω, and 3Ω. They are connected in the shape of a rectangle, with resistances 10Ω and 5Ω forming one side, and resistances 7Ω and 3Ω forming the other side. Another resistance of 10Ω is connected across the diagonal AC.
Step 2: Simplifying the circuit
We can simplify the circuit by reducing the resistances that are in series or parallel. Let's start with the resistances in series.
The resistances 10Ω and 5Ω are in series, so their equivalent resistance is:
R1 = 10Ω + 5Ω = 15Ω
Similarly, the resistances 7Ω and 3Ω are in series, so their equivalent resistance is:
R2 = 7Ω + 3Ω = 10Ω
Now, let's consider the resistance across the diagonal AC. This resistance is in parallel with the resistor R1.
Step 3: Calculating the equivalent resistance
To find the equivalent resistance between points A and B, we need to calculate the total resistance when resistors R2 and the parallel combination of R1 and the diagonal resistance are in series.
The equivalent resistance of the parallel combination of R1 and the diagonal resistance (RD) can be calculated using the formula:
1/RT = 1/R1 + 1/RD
Substituting the values:
1/RT = 1/15Ω + 1/10Ω
Simplifying this expression:
1/RT = (2 + 3)/30Ω
1/RT = 5/30Ω
1/RT = 1/6Ω
Therefore, the equivalent resistance between points A and B is 6Ω.
Step 4: Checking the options
The correct answer is given as 5Ω, which doesn't match the calculated equivalent resistance of 6Ω. Therefore, there might be an error in the given answer options, or the calculations might need to be rechecked.
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Four resistances 10Ω, 5Ω, 7Ω and 3Ω are connected, so that they form the sides of a rectangle AB, BC, CD and DA, respectively. Another resistance of 10Ω is connected across the diagonal AC. The equivalent resistance between A and B isa)2Ωb)5Ωc)7Ωd)10ΩCorrect answer is option 'B'. Can you explain this answer?
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