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Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt?
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Find the power delivered to an element at t=3 ms if the current enteri...
Given Data:
The current entering the positive terminal of the element is given as i = 5cos(πt) A.
The voltage across the element is given as:
(a) v = 3i
(b) v = 3di/dt
Calculation of Power:
The power delivered to an element can be calculated using the equation:
P = vi
For v = 3i:
Substituting the value of v = 3i, we get:
P = (3i)i = 3i^2
For v = 3di/dt:
To calculate the power using v = 3di/dt, we need to find the derivative of i with respect to time (t).
Given i = 5cos(πt), we can differentiate it using the chain rule as follows:
di/dt = -5πsin(πt)
Substituting the value of di/dt = -5πsin(πt) into the equation v = 3di/dt, we get:
v = 3(-5πsin(πt)) = -15πsin(πt)
Now, we can calculate the power as:
P = vi = (-15πsin(πt))(5cos(πt)) = -75πsin(πt)cos(πt)
Calculation at t = 3ms:
To find the power delivered to the element at t = 3ms, we need to substitute t = 3ms into the equations for power.
For v = 3i:
P = 3i^2
Substituting i = 5cos(πt) and t = 3ms (t = 0.003s), we get:
P = 3(5cos(π(0.003)))^2 = 3(5cos(0.003π))^2
For v = 3di/dt:
P = -75πsin(πt)cos(πt)
Substituting t = 3ms (t = 0.003s), we get:
P = -75πsin(π(0.003))cos(π(0.003))
Final Answer:
Substitute the values of P from the above calculations to find the power delivered to the element at t = 3ms.
The current entering the positive terminal of the element is given as i = 5cos(πt) A.
The voltage across the element is given as:
(a) v = 3i
(b) v = 3di/dt
Calculation of Power:
The power delivered to an element can be calculated using the equation:
P = vi
For v = 3i:
Substituting the value of v = 3i, we get:
P = (3i)i = 3i^2
For v = 3di/dt:
To calculate the power using v = 3di/dt, we need to find the derivative of i with respect to time (t).
Given i = 5cos(πt), we can differentiate it using the chain rule as follows:
di/dt = -5πsin(πt)
Substituting the value of di/dt = -5πsin(πt) into the equation v = 3di/dt, we get:
v = 3(-5πsin(πt)) = -15πsin(πt)
Now, we can calculate the power as:
P = vi = (-15πsin(πt))(5cos(πt)) = -75πsin(πt)cos(πt)
Calculation at t = 3ms:
To find the power delivered to the element at t = 3ms, we need to substitute t = 3ms into the equations for power.
For v = 3i:
P = 3i^2
Substituting i = 5cos(πt) and t = 3ms (t = 0.003s), we get:
P = 3(5cos(π(0.003)))^2 = 3(5cos(0.003π))^2
For v = 3di/dt:
P = -75πsin(πt)cos(πt)
Substituting t = 3ms (t = 0.003s), we get:
P = -75πsin(π(0.003))cos(π(0.003))
Final Answer:
Substitute the values of P from the above calculations to find the power delivered to the element at t = 3ms.
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Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt?
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Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt?.
Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the power delivered to an element at t=3 ms if the current entering its positive terminal is i=5cosπt A and the voltage is : (a) v=3i (b)v=3di/dt?.
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