Section A | unit 1 dc circuits

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BEE

Section A

DC Circuits

Question Bank

Q1) Find the current through resistance. Using superposition theorem?

Solution:

1= 0

1 + 2

Q2) Find Current I using superposition theorem?

Sol: 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 Vth and Rth?

Sol:

Finding Isc from circuit directly:

By KCL,

Q4) Find Rth and Vth?

Sol:

Also, clear from circuit that Vth = 1V.

By applying KVL we get,

1-3Isc=0

Isc=A

Q5) Find Rth and Isc?

Sol:

Rth=3k+2k=5k

By applying KVL we get

Therefore,

Q6) Find Vx?

Solution: For Rth

By KCL,

But,

By KVL,

Q7) i?

Find

Solution: Since, no independent source is present so,

Isc = 0

And we know that,

Since Rth cannot be zero

But

Q8) Find out the Norton’s equivalent

Solution:

Since, there is no significance of current source

Q9) For the circuits given below write the voltage equations:

Solution: Let current i1be in loop 1 current and i2 for loop 2

Q10) For the circuits given below write the voltage equations

Solution:

For loop 1

For loop 2

Q11) Using nodal analysis find voltage across 5resistor.

Solution:

For V1

For V2

Solving 1 and 2:

For 5 voltage =

= -50.9 + 57.27

= 6.37V

Q12) Find

Sol:

Q13) Find

Sol:

Q14) Use nodal analysis to find current in the circuit?

Sol: + +3i=4

+ -3i= -3

But i=

Substituting and solving above equation we get

V2 = 10V

i= = 2A

Q15) Find equivalent resistance R?

Sol: Equivalent resistance across ab = = 4Ω

Equivalent resistance across cd = =1 Ω

Req = Rab||Rcd +3 = + 3 = 19/5 Ω

AC Circuits

Q16) For a series RLC circuit having R=10ohms, L= 0.15H, C=100F. They are connected across 100v 50Hz supply. Calculate total impedance?

Sol: Impedance Z=

Z= = 18.27ohm

Q17) For a series RLC circuit having R=12ohms, L= 0.2H, C=60F. They are connected across 100v 50Hz supply. Calculate circuit current?

Sol: I=

Z= = 13.89ohm

I = 100/13.89 =7.2A

Q18) For a series RLC circuit having R=10ohms, L= 0.15H, C=100F. They are connected across 100v 50Hz supply. Calculate power factor?

Sol: cosφ =

Impedance Z=

Z= = 18.27ohm

Cosφ = =

φ = 56.81o lagging

Q19) 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?

Sol: The coil will offer only resistance to dc voltage and impedance to ac voltage

R =24/6 = 4ohm

Z= 30/6 = 5ohm

XL =

= 3ohm

Cosφ = = 4/5 = 0.8 lagging

Q20) 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?

Sol: R=V/I= 4.5/8 = 0.56ohm

At 25Hz Z= V/I=24/8 =3ohm

XL =

= 2.93ohm

XL = 2fL = 2x 25x L = 2.93

L=0.0187ohm

At 50Hz

XL = 2x3 =6ohm

Z = = 5.97ohm

I= 50/5.97 = 8.37A

Power = I2R = 39.28W

Q21) A coil having inductance of 50mH an resistance 10ohmis connected in series with a 25F capacitor across a 200V ac supply. Calculate resonant frequency and current flowing at resonance?

Sol: f0= = 142.3Hz

I0 = V/R = 200/10 = 20A

Q22) A 15mH inductor is in series with a parallel combination of 80ohm resistor and 20F capacitor. If the angular frequency of the applied voltage is 1000rad/s find admittance?

Sol: XL = 2fL = 1000x15x10-3 = 15ohm

XL = 1/C = 50ohm

Impedance of parallel combination Z = 80||-j50 = 22.5-j36

Total impedance = j15+22.5-j36 = 22.5-j21

Admittance Y= 1/Z = 0.023-j0.022 siemens

Q23) 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?

Sol: For series Z =100/0.8 = 125ohm

Cosφ =