The current in the RL-circuit shown below is {i}( {t})=10 \cos (5 {t}-\pi {/}4) {A} The value of the inductor (rounded off to two decimal places) is ....... H.

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 26 of 65

Marks: +1, -0

The current in the RL-circuit shown below is

{i}( {t})=10 \cos (5 {t}-π {/}4) {A}

The value of the inductor (rounded off to two decimal places) is ....... H.

Solution:

Given

V_{s}=200 \cos 5 t

{i}( {t})=10 \cos (5 {t}-\;{π}/{4})

{KVL}

{V}_{ {s}}( {t})= {i}( {t}) {Z}

And

z=R+j ω L=R+j X_{L}

| {Z}|=√{ {R}^{2}+ {X}_{ {L}}^{2}}=\;{ {V}_{ {m}}}/{ {i}_{ {m}}}=\;{200}/{10}

∴ |Z|=20

Or simply

√{R^{2}+X_{L}^{2}}=20

....(i)
Given,

θ=\tan ^{-1}(\;{ω {L}}/{ {R}})=\tan ^{-1}(\;{ {X}_{ {L}}}/{ {R}})

=45^{∘}

∴ \;{ {X}_{ {L}}}/{ {R}}=\tan (45^{∘})=1

∴ {X}_{ {L}}= {R}

......(ii)
From equation (i) and (ii)

√{R^{2}+X_{L}^{2}}=20

√{X_{L}^{2}+X_{L}^{2}}=20

X_{L} √{2}=20

X_{L}=14.14 Ω

ω {L}=14.14

Given

ω=5 {rad} {/} {sec}

∴ {L}=2.828 {H}

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