A resistor 30 Ω , inductor of reactance 10 Ω and capacitor of reactance 10 Ω are connected in series to an AC voltage source e=300√2 sin(ω t) . The current in the circuit is

Question

A resistor 30 Ω , inductor of reactance 10 Ω and capacitor of reactance 10 Ω are connected in series to an AC voltage source e=300√2 sin(ω t) . The current in the circuit is (A)  10√2A  (B)  10 text A  (C)  30√11A  (D)  30√11 text A

Tardigrade Admin · Accepted Answer

e=300√2 sin ω t ... (i) I0=(e0/Z)=(300√2/√(30)2+(10-10)2) ∵ Z=√R2+XL-XC)2 =(300√2/30)=10√2A ∴ Current I=(I0/√2)=10 A

Q. A resistor $30 Ω,$ inductor of reactance $10 Ω$ and capacitor of reactance $10 Ω$ are connected in series to an $A C$ voltage source $e = 3002 s in (ω t)$ . The current in the circuit is

$102 A$

$10 A$

$3011 A$

$3011 A$

5 A

$e = 3002 sin ω t$ ... (i)
$I_{0} = \frac{e _{0}}{Z} = \frac{300 2}{( 30 ) ^{2} + ( 10 - 10 ) ^{2}}$
${∵ Z = R^{2} + X_{L} - X_{C})^{2}}$ $= \frac{300 2}{30} = 102 A$
$∴$ Current $I = \frac{I _{0}}{2} = 10 A$

Q. A resistor 30Ω, inductor of reactance 10Ω and capacitor of reactance 10Ω are connected in series to an AC voltage source e=3002​sin(ωt) . The current in the circuit is

102​A

10A

3011​A

3011​A

5 A

e=3002​sinωt ... (i) I0​=Ze0​​=(30)2+(10−10)2​3002​​ {∵Z=R2+XL​−XC​)2​} =303002​​=102​A ∴ Current I=2​I0​​=10A

Q. A resistor $30 Ω,$ inductor of reactance $10 Ω$ and capacitor of reactance $10 Ω$ are connected in series to an $A C$ voltage source $e = 3002 s in (ω t)$ . The current in the circuit is

$102 A$

$10 A$

$3011 A$

$3011 A$

$e = 3002 sin ω t$ ... (i)
$I_{0} = \frac{e _{0}}{Z} = \frac{300 2}{( 30 ) ^{2} + ( 10 - 10 ) ^{2}}$
${∵ Z = R^{2} + X_{L} - X_{C})^{2}}$ $= \frac{300 2}{30} = 102 A$
$∴$ Current $I = \frac{I _{0}}{2} = 10 A$