A resistor and a capacitor are connected in series to a 10 {V} {dc} supply through a switch is closed at t=0 and the capacitor voltage is found to cross 0 {V} at {t}=0.4 \tau .[\tau= time constant ] . The absolute value of \% change required in the initial capacitor voltage if the zero crossing has to happen at t=0.2 \tau is ________________(rounded off to 2 decimal places).

GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 60 of 65

Marks: +1, -0

A resistor and a capacitor are connected in series to a

10 {V} {dc}

supply through a switch is closed at

t=0

and the capacitor voltage is found to cross

0 {V}

{t}=0.4 τ .[τ=

time constant

] .

The absolute value of

\%

change required in the initial capacitor voltage if the zero crossing has to happen at

t=0.2 τ

is ________________(rounded off to 2 decimal places).

Solution:

we know that voltage across capacitor

V_{c}(t)=V_{c}(∞)+[V_{c}(0)-V_{c}(∞)] e^{-t \/ τ}

In case (i)

0=10+[-V_{1}-10] e^{-0.4 t {/} τ}

0=10+[10+V_{1}] e^{-0.4}

10+V_{1}=10 e^{8.4} . . .(i)

In case (ii)

0=10+[- {V}_{2}-10] {e}^{-0.2}

10+ {V}_{2}=10 {e}^{0.2} . . .

(ii)

(10+ {V}_{1})=10 {e}^{+0.4}

10+ {V}_{1}=10 × 1.491

10+ {V}_{1}=14.91

{V}_{1}=4.91

volt

(10+ {V}_{2})=10 {e}^{0.2}

=10 × 1.221

10+ {V}_{2}=12.21

{V}_{2}=2.21

volt

\%

change in Initial capacitor voltage

\;\; =\;{4.91-2.21}/{4.91} × 100

\;\; =0.5498 × 100=54.98 \% ≈ 55 \%

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