Question 230: AC fundamentals

Question

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5 $$\Omega $$, L=25 mH and C=1000 $$\mu $$F. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

Accepted Answer

It is given that e
0
= 283 V; $$\omega$$ = 320.
The inductor reactance is X
L
= 320 $$	imes$$ 25 $$	imes$$ 10
$$-$$3
= 8 $$\Omega$$
The capacitor reactance is
$${X_C} = {1 \over {\omega C}} = {1 \over {320 	imes 1000 	imes {{10}^{ - 6}}}} = {{1000} \over {320}} = 3.1\,\Omega $$
It is given that R = 5 $$\Omega$$. Therefore, the total impedance is
$$Z = \sqrt {{R^2} + {{({X_L} - {X_C})}^2}}  = \sqrt {50}  = 7\,\Omega $$
and the phase difference between the voltage across the source and the current is
$$	an \phi  = {{{X_L} - {X_C}} \over R} = {{8 - 3.1} \over 5} \approx 1 \Rightarrow 	heta  = 45^\circ $$

Answer

10 $$\Omega $$ and tan$$-$$1 $$\left( {{5 \over 3}} \right)$$

Answer

$$7\,\Omega $$  and 45o

Answer

$$10\,\Omega $$ and tan$$-$$1$$\left( {{8 \over 3}} \right)$$

Answer

$$7\,\Omega $$ and tan$$-$$1$$\left( {{5 \over 3}} \right)$$

AC fundamentals

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5 $\Omega , L=25 mH and C=1000 \mu $F. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

Choose the correct answer: