## 28/02/2021

### Varley Loop Test

• The connection diagram for Varley loop test for both earth fault and short circuit fault is shown in the Figure.
• This test provides for the measurement of total loop resistance.
• The ratio arms P and Q are fixed, balancing of bridge is done by adjusting variable resistance S which is placed in series with the one end of the cable lies inside ground in this test.

Switch K1 connected to position 2

• The variable resistance S is varied till the bridge is balanced.
• Let the variable resistance is S1 for balancing of bridge.

P ( X + S ) = RQ

( P / Q ) = R / ( X + S )

The bridge is balanced at value of S = S1

( P / Q ) = R / ( X + S1 )

( P + Q ) / Q = ( R + X + S1 ) / ( X + S1 )

Therefore ( X + S1 ) = Q ( R + X + S1 ) / ( P + Q )

X = { Q ( R + X + S1 ) / ( P + Q ) }  – S1

= { Q ( R + X + S1 ) }  – S ( P + Q ) / ( P + Q )

= { QR + QX + QS1 – SP – QS1 } / ( P + Q )

= { Q ( R + X ) – PS1 } / ( P + Q ) ………….. ( 1 )

Switch K1 connected to position 1

• The switch K1 is connected to position 1 for earth fault or short circuit in the cable.
• The bridge is again balanced for new value of S = S2.

At balance condition

PS2 = Q ( R + X )

( P / Q ) = ( R + X ) / S2

( R + X ) = PS2 / Q ……….. ( 2 )

From equation ( 1 ) and ( 2 )

X = PS2 – PS1 / ( P + Q )

= P ( S2 – S1 ) / ( P + Q )

As the value of P, Q, S1 and S2 are known, the value of X can be easily calculated.

Loop resistance = R + X = PS2 / Q

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