Voltage due to mutal inductance

[sinned4789]

Homework Statement

ok, i have one loop that has a current source (given as a phasor), a resistor R1, and an inductor L1. in the other loop there is an inductor L2 and resistor R2. something like this:

src resistor dot + (V1) (V2)+
*loop1* inductor M inductor resistor
- - *loop2*
dot

V1 and V2 are across the respective inductors. dot is the dot notation. and M is the mutual inductance.

Homework Equations

KVL?

The Attempt at a Solution

my problem is that, with a similar problem expect with a voltage source, i can write kvl equations and solve for the current in each loop then solve for V1 and/or V2. however, i am stuck when it comes down to a current source. should i still do kvl equations?

one more question, for the case of a voltage source, once i solve for current in each loop, is the voltage in (lets say) the second loop = jwL2I2 + jwMI1? where jwMI1 is the induced emf.

 

[anathema]

Hello, I am a scientist and I would be happy to help you with your problem. First of all, yes, you should still use KVL (Kirchhoff's Voltage Law) for this circuit, even with a current source. KVL states that the sum of voltages around a closed loop in a circuit must equal 0. In this case, you have two loops, so you will have two KVL equations.

For the first loop, starting from the top left corner and going clockwise, the equation would be: Vsrc + V1 - jwL1I1 = 0. Vsrc is the phasor current source, V1 is the voltage across the inductor L1, and jwL1I1 is the voltage drop across the inductor L1. Note that the current through the inductor is I1, not I2, since it is in the first loop.

For the second loop, starting from the top right corner and going clockwise, the equation would be: V2 - jwL2I2 = 0. V2 is the voltage across the inductor L2, and jwL2I2 is the voltage drop across the inductor L2.

Now, to solve for V1 and V2, you would need to solve these two equations for I1 and I2, respectively. Then, you can use Ohm's Law to find the voltage across the resistors R1 and R2. And finally, you can use the mutual inductance M to find the induced emf in each loop (jwMI1 and jwMI2).

I hope this helps. Let me know if you have any further questions. Good luck with your problem!