GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 60 of 65

Marks: +1, -0

0-1

ampere moving iron ammeter has an internal resistance of

50 {m} Ω

and inductance of

0.1 {mH}

. A shunt coil is connected to extend its range to

0-10

Ampere for all operating frequencies. The time constant in milliseconds and resistance in

m Ω

of the shunt coil respectively are

Solution:

For all frequencies time constants of the shunt and meter arm should be equal.
i.e.,

\;{ω L_{m}}/{R_{m}}=\;{ω L_{s h}}/{R_{s h}}

or,

\;{L_{m}}/{R_{m}}=\;{L_{s h}}/{R_{s h}}

or,

\;{L_{m}}/{R_{m}}=\;{0.1 × 10^{-3}}/{50 × 10^{-3}}=0.002

and given,

\;\; I_{m}=1 A, \;\; R_{m}=50 {m} Ω

L_{m}=0.1 {mH}, \;\; I=10 {A}

We know,

\;\; R_{ {sh}}=\;{R_{ {m}}}/{(m-1)} ; \;\; m=\;{I}/{I_{ {m}}}

Here,

\;{10}/{1}=10

∴ \;\; R_{ {sh}}=\;{50 × 10^{-3}}/{10-1}=\;{50 × 10^{-3}}/{9}=5.55 {m} Ω

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