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Current I1,I2,I3 meet at a junction (node) in a circuit. All currents are marked as entering the node. If I1=-6sin(wt) mA and I2= 8cos (wt) maa, then I3 will be?
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Current I1,I2,I3 meet at a junction (node) in a circuit. All currents ...
Calculation of I3 at the Junction
I3 = -6sin(wt) + 8cos(wt) mA
|I3| = sqrt((-6)^2 + 8^2) = 10 mA
phi = tan^-1(-6/8) = -36.87 degrees
Explanation of the Solution
- Using Kirchhoff's Current Law (KCL), the sum of all currents entering the junction should be equal to the sum of all currents leaving the junction.
- Therefore, I1 + I2 = I3
- Substituting the given values of I1 and I2, we get:
I3 = -6sin(wt) + 8cos(wt) mA
- This is the final expression for I3 at the junction.
- It is a function of time, as indicated by the presence of 'wt' in the equation.
- The amplitude of I3 can be found using the Pythagorean theorem:
|I3| = sqrt((-6)^2 + 8^2) = 10 mA
- The phase angle of I3 can be found using the inverse tangent function:
phi = tan^-1(-6/8) = -36.87 degrees
Explanation of the Solution
- The problem involves the application of Kirchhoff's Current Law (KCL) to find the current at a junction in a circuit.
- The current values of I1 and I2 are given in terms of sine and cosine functions, which are periodic functions that repeat themselves after a certain interval.
- The sum of these two functions, I1 + I2, gives the net current entering the junction at any given time.
- The solution involves substituting the given values of I1 and I2 into the KCL equation, and simplifying the expression to obtain I3.
- The amplitude and phase angle of I3 can be found using basic trigonometry.
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Current I1,I2,I3 meet at a junction (node) in a circuit. All currents are marked as entering the node. If I1=-6sin(wt) mA and I2= 8cos (wt) maa, then I3 will be?
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Current I1,I2,I3 meet at a junction (node) in a circuit. All currents are marked as entering the node. If I1=-6sin(wt) mA and I2= 8cos (wt) maa, then I3 will be? 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 Current I1,I2,I3 meet at a junction (node) in a circuit. All currents are marked as entering the node. If I1=-6sin(wt) mA and I2= 8cos (wt) maa, then I3 will be? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Current I1,I2,I3 meet at a junction (node) in a circuit. All currents are marked as entering the node. If I1=-6sin(wt) mA and I2= 8cos (wt) maa, then I3 will be?.
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