Correct Answer - Option 2 : - 0.05%

__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 iron loss component of no-load current or core excitation current.
- The error in the current transformer introduced due to this difference is called the 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.

__Calculation:__

The secondary burden is purely resistive.

∴ cos ϕ = 1,

ϕ = cos^{-1}(1) = 0°

so, δ = 0°

The p.f of the exciting current is 0.5.

cos (90 - α ) = cos^{-1 }(0.5)

90 - α = 60

α = 30

Exciting current I_{0} = 1 A

Nominal Ratio K_{n } = 1000/5 = 200

Since there is no turn compensation, the turn ratio is equal to the nominal ratio or n = K_{n} = 200.

When the primary winding carries a rated current of 1000 A.

Rated secondary I_{s} = 5A

n I_{s} = 200× 5 = 1000 A

Actual transformation ratio,

\(R = n+\frac{I_0}{I_s}sin(δ+ \alpha)=200\ +\ \frac{1}{5}sin(0+30)\)

R = 200.01\(\)

Ratio error = \(\frac{{K_n}-R}{R}\times100\)

= \(\frac{200-200.1}{200.1}\times100\)

=** - 0.05%**