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Two conductors A and B of resistances 5 Ω and 10 Ω respectively are first joined in parallel and then in series. In each case the voltage applied is 20 V. Answer the questions:
In which arrangement will the current through A and B be the same ?
- a)Series arrangement
- b)Parallel arrangement
- c)Both of the above
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two conductors A and B of resistances 5 Ω and 10 Ω respectively are f...
Explanation:
When two resistors are connected in parallel, the potential difference across each resistor is the same and equal to the applied voltage.
When two resistors are connected in series, the current passing through each resistor is the same.
Let's calculate the current passing through the resistors in both cases.
Parallel arrangement:
The equivalent resistance of the parallel combination of resistors is given by:
1/R = 1/R1 + 1/R2
1/R = 1/5 + 1/10
1/R = 1/3.33
R = 3.33 Ω
The current passing through the resistors in parallel is given by:
I = V/R
I = 20/3.33
I = 6 A
The current passing through resistor A in parallel is:
I(A) = V/R1
I(A) = 20/5
I(A) = 4 A
The current passing through resistor B in parallel is:
I(B) = V/R2
I(B) = 20/10
I(B) = 2 A
Therefore, the current passing through A and B is not the same in the parallel arrangement.
Series arrangement:
The equivalent resistance of the series combination of resistors is given by:
R = R1 + R2
R = 5 + 10
R = 15 Ω
The current passing through the resistors in series is given by:
I = V/R
I = 20/15
I = 1.33 A
The current passing through resistor A in series is:
I(A) = V/R1
I(A) = 20/5
I(A) = 4 A
The current passing through resistor B in series is:
I(B) = V/R2
I(B) = 20/10
I(B) = 2 A
Therefore, the current passing through A and B is the same in the series arrangement.
Hence, the correct answer is option 'A'. The current passing through A and B will be the same in the series arrangement.
When two resistors are connected in parallel, the potential difference across each resistor is the same and equal to the applied voltage.
When two resistors are connected in series, the current passing through each resistor is the same.
Let's calculate the current passing through the resistors in both cases.
Parallel arrangement:
The equivalent resistance of the parallel combination of resistors is given by:
1/R = 1/R1 + 1/R2
1/R = 1/5 + 1/10
1/R = 1/3.33
R = 3.33 Ω
The current passing through the resistors in parallel is given by:
I = V/R
I = 20/3.33
I = 6 A
The current passing through resistor A in parallel is:
I(A) = V/R1
I(A) = 20/5
I(A) = 4 A
The current passing through resistor B in parallel is:
I(B) = V/R2
I(B) = 20/10
I(B) = 2 A
Therefore, the current passing through A and B is not the same in the parallel arrangement.
Series arrangement:
The equivalent resistance of the series combination of resistors is given by:
R = R1 + R2
R = 5 + 10
R = 15 Ω
The current passing through the resistors in series is given by:
I = V/R
I = 20/15
I = 1.33 A
The current passing through resistor A in series is:
I(A) = V/R1
I(A) = 20/5
I(A) = 4 A
The current passing through resistor B in series is:
I(B) = V/R2
I(B) = 20/10
I(B) = 2 A
Therefore, the current passing through A and B is the same in the series arrangement.
Hence, the correct answer is option 'A'. The current passing through A and B will be the same in the series arrangement.
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Two conductors A and B of resistances 5 Ω and 10 Ω respectively are f...
Through (a)Series as the current remains same in the series arrangement
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Two conductors A and B of resistances 5 Ω and 10 Ω respectively are first joined in parallel and then in series. In each case the voltage applied is 20 V. Answer the questions:In which arrangement will the current through A and B be the same ?a)Series arrangementb)Parallel arrangementc)Both of the aboved)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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