We use Varley loop test to find out the fault location of an underground cable. Like Murray loop test, we also apply a Wheatstone bridge circuit to perform the Varley loop test. Unlike in Murray loop test circuit, in later we use prefixed ratio arms of the bridge. That means we cannot change the resistance value of the ratio arms during measurement. In addition to that, we insert a variable resistance in series with the faulty cable at its head.

### Varley Loop Test for Finding Ground Fault Location

In the circuit of the test, a sound cable runs in parallel with the faulty cable. We connect the far end of both faulty and sound cable through a short circuit path. Then we provide a battery between the junction of the ratio arms and the ground. Because in that case, we have assumed there is a ground fault in the cable. After arranging everything, we have to adjust the value of the variable resistance until the galvanometer shows zero deflection. When we achieve the zero deflection in the galvanometer we can say that the Varley loop test circuit has reached to its balanced condition.

Let us assume, the value of the variable resistance is Y at the balanced condition of the circuit. Now as per the theory of Wheatstone bridge, we can write,

Where X is the resistance between the operating head of the cable and its faulty point. R is the resistance between the rest portion of the faulty cable plus that of the sound cable.

Since we already know the value of the ratio A / B. Also, we know the value of Y because we ourselves have adjusted the value. R + X is the resistance of the series combination of faulty and sound cable. So, we can also find it out from the cable data sheet.

If the ratio A / B is unity (i.e. 1), we can write,

So, we can easily calculate the value of X from the above equation of Varley Loop test. Hence, we can calculate the distance of the fault as the resistance per unit length of the cable conductor is provided in the datasheet of the cable.

Where r is the resistance per unit length of the cable conductor.

### Varley Loop Test for Finding Short Circuit Fault Location

Here, instead of connecting the battery end to the ground, we will connect it with the head of the other short-circuited cable. Other arrangements of the test are the same as in the previous case of Varley loop test where we found out a ground fault location.

#### Varley Loop Test for Short Circuit Fault

Here also after adjusting the variable resistance, we have to obtain null deflection of the galvanometer. At that balanced condition of the circuit, we can write the same equation as follows.

Naturally, from the above equation, we can find out the resistance of the portion of the faulty cable between operating location and short circuit point. Hence from that resistance, we can easily calculate the distance of the faulty location from the operating location.

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