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  • In the circuit shown, the AC source has voltage <img alt="\mathrm{\mathrm{V}=20 \cos (\omega \mathrm{t}) \text { volt with } \omega=2000 \mathrm{rads}^{-1}}" src="https://entrancecorner.oncode

In the circuit shown, the AC source has voltage \mathrm{\mathrm{V}=20 \cos (\omega \mathrm{t}) \text { volt with } \omega=2000 \mathrm{rads}^{-1}} , the amplitude of the current will be nearest to:
                  

Option: 1

2 A


Option: 2

3.3 A


Option: 3

2 / \sqrt{5} \mathrm{~A}


Option: 4

\sqrt{5} \mathrm{~A}


Answers (1)

best_answer

Total resistance of the circuit \mathrm{\mathrm{R}=6+4=10 \Omega }
Capacitive reactance 
\mathrm{\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{2000 \times 50 \times 10^{-6}}=10 \Omega }
Inductive reactance 
\mathrm{\mathrm{X}_{\mathrm{L}}=\omega \mathrm{L}=2000 \times 5 \times 10^{-3}=10 \Omega }
\mathrm{\therefore \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}=10 \Omega }
\mathrm{Amplitude of current \mathrm{I}_0=\frac{\mathrm{V}_0}{\mathrm{Z}}=\frac{20}{10}=2 \mathrm{~A} }

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