# Balance condition for inductor bridge

1. Aug 26, 2009

### 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

2. Relevant equations
$$E.M.F=L*di/dt$$

all equations of transient current in the circuit.

I couldnt generate one at all , even writing the current equations using KVL because they are time dependent.

2. Aug 26, 2009

### 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?

3. Aug 26, 2009

### zd1899

IF it was DC, wont we consider a time variant state?

4. Aug 27, 2009

### vk6kro

No, DC is constant with zero frequency. The question lets 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 text books 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.