XL | unit 1 dc ac circuits

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BEE

UNIT – 1DC AND AC CIRCUITS Q1) Find the current through

resistance. Using superposition theorem?

A1)

1= 0

1 + 2

Q2) Find Current I using superposition theorem?

A 2)Since two voltage sources with different magnitude in parallel which cannot be connected as in single branch two different current is not possible (if 5V than I = zero).

1 =

2 =

1 + 2

Q3) Find i?

A 3) Since, no independent source is present so, Isc = 0And we know that,

Since Rth cannot be zero

But

Q4) For the circuits given below write the voltage equations:

A 4) Let current i1be in loop 1 current and i2 for loop 2

Q5) For the circuits given below write the voltage equations

A 5)

For loop 1

For loop 2

Q6) Using nodal analysis find voltage across 5resistor.

A 6)

For V1

……..(1) For V2

…..(2) Solving 1 and 2:

For 5 voltage =

Q 7) Find

A 7)

Q8) Find

A 8)

Q9) Use nodal analysis to find current in the circuit?

A 9)

But

Substituting and solving above equation we get

Q10) Find equivalent resistance R?

A 10)Equivalent resistance across ab =

= 4ΩEquivalent resistance across cd =

=1 ΩReq = Rab||Rcd +3 =

+ 3 = 19/5 Ω AC CIRCUITS Q11) For a series RLC circuit having R=10ohms, L= 0.15H, C=100

F. They are connected across 100v 50Hz supply. Calculate total impedance?A 11)Impedance Z=

= 18.27ohm Q12) For a series RLC circuit having R=12ohms, L= 0.2H, C=60

F. They are connected across 100v 50Hz supply. Calculate circuit current?A 12) I=

= 13.89ohmI = 100/13.89 =7.2A Q13) For a series RLC circuit having R=10ohms, L= 0.15H, C=100

F. They are connected across 100v 50Hz supply. Calculate power factor?A13) cosφ =

Impedance Z=

= 18.27ohmcosφ =

φ = 56.81o lagging Q14) A coil takes a current of 6A when connected to 24V dc supply. To obtain the same current with 50HZ ac, the voltage required was 30V. Calculate inductance and p.f of coil?A14) The coil will offer only resistance to dc voltage and impedance to ac voltageR =24/6 = 4ohmZ= 30/6 = 5ohm

XL =

= 3ohm

cosφ =

= 4/5 = 0.8 lagging Q15) The potential difference measured across a coil is 4.5V,when it carries a dc current of 8A. The same coil when carries ac current of 8A at 25Hz,the potential difference is 24V. Find current and power when supplied by 50V,50Hz supply?A15) R=V/I= 4.5/8 = 0.56ohmAt 25Hz Z= V/I=24/8 =3ohm XL =

At 50HzXL = 2x3 =6ohmZ =

= 5.97ohmI= 50/5.97 = 8.37APower = I2R = 39.28W Q16) A coil having inductance of 50mH an resistance 10ohmis connected in series with a 25

F capacitor across a 200V ac supply. Calculate resonant frequency and current flowing at resonance?A16) f0=

= 142.3HzI0 = V/R = 200/10 = 20A Q17) A 15mH inductor is in series with a parallel combination of 80ohm resistor and 20

F capacitor. If the angular frequency of the applied voltage is 1000rad/s find admittance?A 17) XL = 2

fL = 1000x15x10-3 = 15ohm XL = 1/

C = 50ohmImpedance of parallel combination Z = 80||-j50 = 22.5-j36Total impedance = j15+22.5-j36 = 22.5-j21Admittance Y= 1/Z = 0.023-j0.022 siemens Q18) A circuit connected to a 100V, 50 Hz supply takes 0.8A at a p.f of 0.3 lagging. Calculate the resistance and inductance of the circuit when connected in series and parallel?A18) For series Z =100/0.8 = 125ohmcosφ =

R = 0.3 x 125 = 37.5ohmXL =

= 119.2ohm XL = 2

fL = 2

x 50x L 119.2 = 2

x 50x LL= 0.38HFor parallel:Active component of current = 0.8 cosφ = 0.3x0.3 = 0.24A R = 100/0.24 =416.7ohmQuadrature component of current = 0.8 sinφ = 0.763XL= 100/0.763 = 131.06ohmL= 100/0.763x2

x50 = 0.417H Q19) Calculate impedance of a parallel tuned RC circuit at a frequency of 400kHz and for a BW of operation equal to 20kHz. Given R=5ohm?A19) BW =R/2

L L= 39

Hf0 =

C = 2.6x10-9FZ= L/RC = 3kohm Q20) Three similar resistors are connected in star across 400V 3-phase lines. Line current is 4A. Calculate the value of each resistor.A 20) For star connection:IL=Iph=4AVph=VL/

= 400/

= 231VRph= 231/4= 57.75ohm For Delta Connection:IL=4AIph= IL/

=4/

==2.30AZph=400/2.30=173.9ohmRph= 173.9/3 = 57.97ohm

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