1. When a direct current of 2A is passed through a coil, the potential difference across the coil is 20V. When an alternating current of 2A at a frequency of 40Hz is passed through a coil, the potential difference across the coil is 140V. Find the current in the coil if it is connected to a 230V, 50Hz supply.
When direct current is passed, only resistance will come into picture.
Hence, coil resistance R =V/I = 20/2 =10 ohms.
When AC is passes, inductance will also come into picture.
V=IZ
----(1)
We have to find current when 230V at 50 Hz is applied across the coil. Let the current be I. we will have
---- (2)
We will determine L from (1) and put this value of in (2) to determine I.
Hence, , say 2.64A.
2. A circuit consists of 3 blocks connected in series. The first block consists of a resistor 31 ohms and a capacitor 100 microfarads connected in parallel. The second block consists of a resistor 50 ohms. The third block of a resistor 20 ohms and an inductance 0.11 henry connected in parallel. The circuit is connected to a 230V 50Hz supply. Determine the overall current taken from the supple and its phase using complex notations.
We make the following figure to solve this problem. The following circuit is drawn in Multisim and we see that current is 2.833amps. Any we will calculate it.
Hence, same value as we got through Multisim.
3. A 100 ohm resistor is connected to a 100V 50Hz power source. At the initial moment of time t = 0, the instantaneous value of the voltage was zero, and that of the current was 0.7A. Determine:
a) Phase shift φ between voltage and current.
V = 100 volt
Hence, we can write as v is zero at t =0.
If θ is phase difference, we have
Or, , say 300.
b) Time interval Δt which corresponds to this phase shift.
Frequency = 50Hz; period = 360 degrees = 1/50 = 20 mili-secs.
Hence, 30 degrees = (30/360)*20 = 1.666 mili-secs.
c) Power factor = cos 30 = 0.866
d) Apparent power =VI = 100*(100/100) = 100VA
e) Active power consumed in the resistor = VI = 100*1= 100W.