Solve Series Circuit: 10V Current Calculations

[magnifik]

Homework Statement

RESOLVEDRESOLVEDRESOLVEDRESOLVEDRESOLVEDRESOLVEDRESOLVEDRESOLVED
the fact that the source voltage is 10 V is given, and i need to find the current through this voltage.

Homework Equations

Ldi/dt + IR = v0coswt
w = omega but i don't know how to do the special symbols

The Attempt at a Solution

i tried finding the total inductance and total resistance first
i got L = .016 and R = 2.5
so now i have .016di/dt + I(2.5) = 10cos(625t) and basically i don't know what to do after that

am i using the wrong equation or getting the wrong values for L and R?

 

[berkeman]

Homework Statement

http://img52.imageshack.us/img52/8089/74283078.jpg
this is a series RL circuit problem. the fact that the source voltage is 10 V is given, and i need to find the current through this voltage.

Homework Equations

Ldi/dt + IR = v0coswt
w = omega but i don't know how to do the special symbols

The Attempt at a Solution

i tried finding the total inductance and total resistance first
i got L = .016 and R = 2.5
so now i have .016di/dt + I(2.5) = 10cos(625t) and basically i don't know what to do after that

am i using the wrong equation or getting the wrong values for L and R?

Youre value for the parallel combination of the inductors is correct, but your value for the series combination of the resistors is incorrect. Check that part again.

You are correctly writing the form of the differential equation to solve for I(t). Once you fix the resistance value, just solve it like you normally would solve for a differential equation with a sinusoid involved.

Or, you could use phasor math instead. Are you familiar with how to use the complex impedances in the circuit to solve using the phasor method?

 

[magnifik]

is R 10? is it not parallel?
i am not familiar with the phasor method.

 

[rl.bhat]

When you connect LR circuit to a sinusoidal voltage, the inductive reactance XL = ω*L
and total impedance of the circuit is
Z = sqrt(R^2 + XL*2). And
i(rms) = V(rms)/Z.

 

[magnifik]

When you connect LR circuit to a sinusoidal voltage, the inductive reactance XL = ω*L
and total impedance of the circuit is
Z = sqrt(R^2 + XL*2). And
i(rms) = V(rms)/Z.

does this equation work for the problem even though it says to find I_{s max?}

 

[rl.bhat]

Yes.

 

[magnifik]

okay is this right...
Z=sqrt[R^2 + XL^2]
R = 10
XL = 625 * .016 = 10
Z=sqrt[200]
Z=14.1421
I = V/Z
I = 10/14.1421 = .7071 A

 

[vela]

is R 10? is it not parallel?

The resistors are not in parallel. For two elements to be in parallel, the ends of each component need to be connected to the same two nodes. The two inductors, for example, are in parallel because one end of both inductors is connected to the top dot, and the other end is connected to the bottom dot. The resistors, on the other hand, are not in parallel. The right end of the top resistor is connected to the top dot while the right end of the bottom resistor is connected to the bottom dot.

The resistors and the voltage source are connected in series: they are connected end to end, and all the current that goes through one element goes through the others as well.