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A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A?
Most Upvoted Answer
A direct current of 10A is superimposed on an alternating current I=40...
Irms for DC = 10A
Irms for AC = 40/√2 A
resultant I rms = √{(10)² + (40/√2)²}
= √{100 + (1600/2)}
= √(1800/2)
=√900
= 30 A
Irms for AC = 40/√2 A
resultant I rms = √{(10)² + (40/√2)²}
= √{100 + (1600/2)}
= √(1800/2)
=√900
= 30 A
Community Answer
A direct current of 10A is superimposed on an alternating current I=40...
Problem Analysis:
We are given an alternating current (AC) of the form I = 40*cos(wt), where I is the current and wt represents angular frequency, and a direct current (DC) of 10A. We need to find the effective value of the resulting current.
Solution:
To find the effective value of the resulting current, we need to calculate the root mean square (RMS) value. The RMS value is given by the formula:
I_RMS = sqrt(I_1^2 + I_2^2 + 2*I_1*I_2*cos(θ))
where I_1 and I_2 are the magnitudes of the two currents and θ is the phase difference between them.
In this case, the AC current is given by: I = 40*cos(wt)
And the DC current is given by: I = 10
Therefore, I_1 = 40 and I_2 = 10
The phase difference between the AC and DC currents is 0 degrees, as they are in phase with each other.
Plugging in the values into the RMS formula:
I_RMS = sqrt((40^2) + (10^2) + 2*40*10*cos(0))
Simplifying the equation:
I_RMS = sqrt(1600 + 100 + 2*400*1)
I_RMS = sqrt(1600 + 100 + 800)
I_RMS = sqrt(2500 + 800)
I_RMS = sqrt(3300)
I_RMS ≈ 57.45 A
Therefore, the effective value of the resulting current is approximately 57.45 A.
Answer: The effective value of the resulting current is approximately 57.45 A.
We are given an alternating current (AC) of the form I = 40*cos(wt), where I is the current and wt represents angular frequency, and a direct current (DC) of 10A. We need to find the effective value of the resulting current.
Solution:
To find the effective value of the resulting current, we need to calculate the root mean square (RMS) value. The RMS value is given by the formula:
I_RMS = sqrt(I_1^2 + I_2^2 + 2*I_1*I_2*cos(θ))
where I_1 and I_2 are the magnitudes of the two currents and θ is the phase difference between them.
In this case, the AC current is given by: I = 40*cos(wt)
And the DC current is given by: I = 10
Therefore, I_1 = 40 and I_2 = 10
The phase difference between the AC and DC currents is 0 degrees, as they are in phase with each other.
Plugging in the values into the RMS formula:
I_RMS = sqrt((40^2) + (10^2) + 2*40*10*cos(0))
Simplifying the equation:
I_RMS = sqrt(1600 + 100 + 2*400*1)
I_RMS = sqrt(1600 + 100 + 800)
I_RMS = sqrt(2500 + 800)
I_RMS = sqrt(3300)
I_RMS ≈ 57.45 A
Therefore, the effective value of the resulting current is approximately 57.45 A.
Answer: The effective value of the resulting current is approximately 57.45 A.
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A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A?
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A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A?.
A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A direct current of 10A is superimposed on an alternating current I=40Coswt flowing through a wire. The effective value of the resulting current will be A) 10√2 A B) 20√2 A C) 20√3 A D) 30 A?.
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