Balance condition for inductor bridge

[zd1899]

1. A Wheat stone bridge resembling setup is given with two parallel branches , the 1st containing an Inductor of Inductance L1 and resistance R1 in series with a resistor R2.
The second branch consists of inductor with inductance L2 and resistance R3 in series with a resistor R4. The branches are connected through the middle by a galvanometer making it resemble a Wheat stone bridge.
Find the balance condition

Homework Equations

$$E.M.F=L*di/dt$$

all equations of transient current in the circuit.


I couldn't generate one at all , even writing the current equations using KVL because they are time dependent.

 

[vk6kro]

This is potentially a difficult problem. Depending on the resistances of the inductors, you may not get a balance point at all.


There is a possible trick to this question though. Not sure if it was intentional.
Galvanometers don't work on AC, so you have to feed the bridge with DC.
This makes the inductors vanish and you have a simple 4 resistor Wheatstone Bridge.

Maybe you could check to see if this was the intention?

 

[zd1899]

IF it was DC, won't we consider a time variant state?

 

[vk6kro]

No, DC is constant with zero frequency. The question let's you choose the frequency and you must choose DC to make the galvanometer work.

The reactance of the inductors is XL = 2 * pi * F * L.
If F is zero, then XL is zero too and only the resistance of the coil matters.

The measurement of reactance with LCR bridge circuits would be covered in most textbooks on AC theory, so you can just look it up if the Galvanometer turns out to be a mistake and an oscilloscope or other AC detector is substituted.