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Current I1, I2 and 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) mA, then I3 will be?


a) 10 cos(wt 36.87) mA
b) 14 cos(wt 36.87) mA
c) -14 sin(wt 36.87) mA
d) -10 cos(wt 36.87) mA Correct answer is option d.?
Most Upvoted Answer
Current I1, I2 and I3 meet at a junction (node) in a circuit. All curr...
Alll the current entering the node so, i1+i2+i3=0, therefore i3=-(i1+i2), i3=-(-6sinwt+8coswt)
{since, asinx+bcosx=√ a^2+b^2 sin(x+y) and tany=b/a}
i3=-[√(-6) ^2+(8) ^2 sin( wt-53.13)] { since y =tan-1 (-8/6) = -53.13}
i3=-[10 cos( wt+(90-53.13))]
i3= -10 cos( wt+ 36.87) ~> option (d)
Community Answer
Current I1, I2 and I3 meet at a junction (node) in a circuit. All curr...
Solution:

To determine I3, we will use Kirchhoff's Current Law which states that the sum of all currents entering and leaving a node is equal to zero.

I1 + I2 + I3 = 0

Substituting the given values of I1 and I2:

-6sin(wt) + 8cos(wt) + I3 = 0

Rearranging the equation:

I3 = 6sin(wt) - 8cos(wt)

We can use trigonometric identities to simplify this equation:

I3 = 10cos(wt - 36.87°)

Therefore, the correct answer is option d) -10 cos(wt 36.87) mA.

Explanation:

- Kirchhoff's Current Law is introduced as the first point of the solution.
- The given values of I1 and I2 are substituted in the equation.
- The equation is rearranged to isolate I3 and simplify it using trigonometric identities.
- The final answer is presented with the correct option.
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Current I1, I2 and 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) mA, then I3 will be? a) 10 cos(wt 36.87) mAb) 14 cos(wt 36.87) mA c) -14 sin(wt 36.87) mA d) -10 cos(wt 36.87) mA Correct answer is option d.?
Question Description
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