• Kelvin's double bridge is used to measure low resistances because the effect of contact and lead resistance is eliminated
• Kelvin double bridge incorporates the idea of the second set of ratio arms and uses four-terminal resistors
• The effect of thermo-electric emfs can be eliminated by making another measurement with the battery connections reversed

Concept:

• A Wheatstone bridge is a special arrangement of 4 resistors. It can be used to find an unknown resistance.
• If the Wheatstone bridge is balanced, there will be no current flowing through the galvanometer.

• Wheatstone bridge is used to measure the resistance with the help of a comparison method.
• The Wheatstone bridge work on the principle of null deflection.

​The bridge is balanced when: \(\frac{P}{R}=\frac{Q}{S}\)

Calculation:

Given that,

For a whetstone network, we have four resistance P, Q, R, and S, and their values are

P = 25 Ω

Q = 15 Ω

R = 17 Ω

S =?

Balanced bridge: The bridge is said to be balanced when deflection in the galvanometer is zero i.e. no current flows through the galvanometer. 

In the balanced condition \(\frac{P}{R} = \frac{Q}{S}\), on mutually changing the position of cell and galvanometer, this condition will not change.

\(S=\frac{QR}{P}\)

\(= \frac{15\times 17}{25}\)= 10.2 Ω

• Both Maxwell's and Anderson's bridges are used for the measurement of inductance.

​Note:

De-Sauty bridge:

The de-Sauty bridge is suitable for the measurement of pure capacitance.

Let, 

Z₁ = R₁

Z₂ = R₂ 

\(Z_3=\frac{1}{jω C}\)

\(Z_x=\frac{1}{jω C_x}\)

At bridge balance condition, 

Z₁ Z₃ = Z₂ Z_x

\(\frac{1}{jω C}\times R_1 =R_2\times \frac{1}{jω C_x}\)

⇒ \( {C_x}{R_1}=C{R_2}\)

∴ \({C_x} = C\left( {\frac{{{R_2}}}{{{R_1}}}} \right)\)

Points to remember:

Modified De-Sauty bridge is used to find impure capacitance and Dissipation factor (D-factor)

D-factor = ω R_x C_x

R_x = Resistance of C_x (impure)

For De-Sauty's bridge, D-factor is zero because of pure capacitance (R_x = 0). 

Megger:

• Megger is a portable instrument that is used to measure the insulation resistance of the electrical machinery or system.
• It can be battery operated or mechanically operated (hand crank dc generator) and gives a direct reading in ohms.
• It basically works on the principle of electromagnetic induction.
• The electrical power to a megger is provided by a permanent magnet D.C. generator.
• The operating voltage of a megger is about 50 to 100 V.

Points to remember:

• Megger is also called an insulation tester because it is used to measure the insulation resistance of underground cables, motor windings, etc.
• The loss of charge method also used to measure the insulation resistance in MΩ.

Ratio error in current transformer:

• In the current transformer, the primary current Ip should be exactly equal to the secondary current multiplied by turns ratio, i.e. KTIs.
• But there is a difference between primary current Ip should be exactly equal to the secondary current multiplied by the turns ratio.
• This difference is contributed by the core excitation or magnetizing component of no-load current.
• The error in the current transformer introduced due to this difference is called current error or ratio error.

The actual ratio of transformation varies with operating conditions and the error in secondary voltage is defined as

Percentage ratio error \( = \frac{{{K_n} - R}}{R} \times 100\)

Kn is the nominal ratio

R is the actual ratio

It can be reduced by secondary turns compensation i.e. slightly decreasing the secondary turns.

Phase angle error:

In an ideal voltage transformer, there should not be any phase difference between the primary voltage and the secondary voltage reversed. However, in an actual transformer, there exists a phase difference between Vo­ and V­s reversed.

The phase angle is taken as +ve when secondary voltage reversed leads the primary voltage.

The angle is -ve when the secondary voltage reversed lags the primary voltage.

It can be reduced by keeping the primary and secondary windings are wound as closely as possible.

Secondary side of current transformer is always kept short circuited in order to avoid core saturation and high voltage induction, so that current transformer can be used to measure high values of currents.

• Current transformer works on the principle of shorted secondary.
• It means that burden on the system Zb is equal to 0.
• Thus, current transformer produces a current in its secondary which is proportional to the current in its primary.

Important Points:

• Most important precaution in use of a CT is that in no case should it be open circuited (even accidently).
• As the primary current is independent of the secondary current, all of it acts as a magnetizing current when the secondary is opened.
• This results in deep saturation of the core which cannot be returned to the normal state and so the CT is no longer usable.
• Again, due to large flux in the core the flux linkage of secondary winding will be large which in turn will produce a large voltage across the secondary terminals of the CT.
• This large voltage across the secondary terminals will be very dangerous and will lead to the insulation failure and there is a good chance that the person who is opening the CT secondary while primary is energized will get fatal shock.

• Varley loop test is used for locating short-circuit and earth faults in underground cables.
• This test also employs the principle of the Wheatstone bridge. However, the difference between Murray loop test and Varley loop test is that, in Varley loop test resistances R₁ and R₂ are fixed, and a variable resistor is inserted in the faulted leg.
• If the fault resistance is high, the sensitivity of Murray loop test is reduced, and Varley loop test may be more suitable.