In the circuit shown, if {v}( {t})=2 \sin (1000 {t}) volts, {R}=1 {k} Ω and {C}=1 {\muF}, then the steady-state current {i}( {t}), in milliamperes ( {mA}), is

Correct Answer is : 3sin(1000t)+cos(1000t)

2 \sin (1000 t)+2 \cos (1000 t)

GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 46 of 65

Marks: +1, -0

In the circuit shown, if

{v}( {t})=2 \sin (1000 {t})

volts,

{R}=1 {k} Ω

and

{C}=1 {µF}

, then the steady-state current

{i}( {t})

, in milliamperes

( {mA})

, is

Solution:

Performing star to delta conversion

Where

{Z}_{1}=2[\;{ {R}}/{1+\;{ {jWCR}}/{3}}]

∴ {Z}_{ {eq}}= {Z}_{1} (\;{ {R}}/{1+\;{ {jWCR}}/{3}})

∴ {Z}_{ {eq}}=\;{2}/{3}(\;{ {R}}/{1+\;{ {jWCR}}/{3}})

Now

{R}=1 {kW}, {C}=1 µ {F}

and

{W}=1000 {rad} \/ {sec}

∴ {Zeq}=0.66-0.2178 {j}

∴ {I}=\;{ {V}}/{ {Z}_{ {eq}}}

=\;{2 \sin (1000 t)}/{0.66-0.2178 {j}}

=\;{2}/{√{0.66^{2}+0.2178^{2}}} ⋅ \sin (1000 t-\tan ^{-1}(\;{1}/{3}))

=3.16 \sin (1000 t+18.43^{∘})

∴ I ≈ 3 \sin (1000 t)+\cos (1000 t)

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