Alternating Current - Numerical - Solved

Great Mind

1. A coil of inductance 80 mH and resistance 60 W is connected to a 200 V, 100 Hz supply.

    Calculate the circuit impedance and the current taken from the supply. Find also the phase angle

    between the current and the supply voltage.

ans:

Here;

From the triangle,

Now,

This way phase angle can be calculated.

2.An alternating voltage given by v = 100 sin 240t volts is applied across a coil of resistance 32 W 

    and inductance 100 mH. Determine (a) the circuit impedance, (b) the current flowing, (c) the p.d. 

    across the resistance, and (d) the p.d. across the inductance.

ans:

a) -->

Now

Finally,

3. A coil takes a current of 5 A from a 20 V d.c. supply. When connected to a 200 V, 50 Hz a.c. 

    supply the current is 25 A.  Calculate the (a) resistance, (b) impedance and (c) inductance of the 

    coil.

ans

4. A resistor and an inductor of negligible resistance are connected in series to an a.c. supply. The 

     p.d. across the resistor is 18 V and the p.d. across the inductor is 24 V. Calculate the supply voltage 

     and the phase angle between voltage and current.      

ans:

                          

(Make an imaginary triangle in your mind before solving the problems involving phase calculation.)

5.A coil of inductance 636.6 mH and negligible resistance is connected in series with a 100 W 

    resistor to a 250 V, 50 Hz supply. Calculate (a) the inductive reactance of the coil, (b) the 

    impedance of the circuit, (c) the current in the circuit, (d) the p.d. across each component, and 

    (e) the circuit phase angle.

ans:

Making an equivalent circuit.

6.

Two similar capacitors are connected in parallel to a 200 V, 1 kHz supply. Find the value of 

       each capacitor if the current is 0.628 A.

ans:

7.A resistance of 50 W is connected in series with a capacitance of 20 mF. If a supply of 200 V, 

    100 Hz is connected across the arrangement find (a) the circuit impedance, (b) the current 

    flowing, and (c) the phase angle between voltage and current.

ans:

Making equivalent circuit

8. A 24.87 μF capacitor and a 30 W resistor are connected in series across a 150 V supply. If the current 

     flowing is 3 A find (a) the frequency of the supply, (b) the p.d. across the resistor and (c) the p.d. across the            

     capacitor.     

ans:

                                                                       

9. An alternating voltage v = 250 sin 800t volts is applied across a series circuit containing a 30 W 

    and 50 mF capacitor. Calculate (a) the circuit impedance, (b) the current flowing, (c) the p.d. 

   across the resistor, (d) the p.d. across the capacitor, and (e) the phase angle between voltage and 

   current.

ans:

        Making equivalent circuit.

10. A 400 W resistor is connected in series with a 2358 pF capacitor across a 12 V a.c. supply. 

     Determine the supply frequency if the current flowing in the circuit is 24 mA.

ans:

Making equivalent circuit,

That's it Guys!

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