Three impedances zi zz zz are connected in parallel across a...

Three impedances Z1, Z2, Z3 are connected in parallel across a 230V, 50 Hz supply. The values are given Z1 = 12 ∠30°, Z2 = 8 ∠-30°, Z3 = 10 ∠60°. Calculate the total admittance, equivalent impedance, total current, power factor, and power consumed by the whole circuit.

Transcript

00:01 In this question it is given that the voltage v is equal to 40 multiplied with cos of 100 t volts.

00:10 And z1 is equal to what? equals to 10 ohms.

00:14 And z2 is equal to what? it is equal to 20 plus j multiplied with 20.

00:22 And z3 is equal to what? it is equal to 3 minus j multiplied with 40.

00:30 Okay.

00:30 So therefore in the part a of the problem, the admittance, alright, we mark it as a equals to what is given as y is equal to 1 divided by x.

00:41 Alright.

00:42 So first we have what? first we have 1 divided or therefore y1 equals to what? y1 equals to 1 divided by 10.

00:54 That is equal to 0 decimal 1 and the unit will be what? it will be mo.

00:59 Alright.

01:00 So next y2 equals to what? y2 equals to 1 divided by under root 20 square plus 20 square.

01:09 Alright.

01:09 So this is equal to what? this is equal to how much? this is equal to 0 decimal 0353 and the unit will be mo or we can call it siemens.

01:20 Alright.

01:20 So finally we will have y3 that is equal to what? that is equal to 1 divided by or 3 square plus 40 square.

01:29 Alright.

01:29 So this is equal to what? this is equal to 0 decimal 0219 siemens.

01:37 Alright.

01:37 So now finally we get therefore now we will find out what? we will find out the conductance.

01:46 Alright.

01:46 So therefore conductance is equal to what? conductance equals to 1 divided by r that is the resistance.

01:53 Alright.

01:54 So we write therefore g1 and conductance is denoted by g.

01:58 Alright.

01:59 So g1 equals to what? g1 equals to 1 divided by 10 that is equal to 0 decimal 1 siemens.

02:07 Alright.

02:08 G2 is equal to what? it is equal to 1 divided by 20 that is equal to 0 decimal 057.

02:16 Alright.

02:17 And finally we have g3 that is equal to what? that is equal to 1 divided by 3.

02:24 Alright.

02:25 Which is equal to 0 decimal 337.

02:28 Okay.

02:29 Therefore, we can say that these three are the answers for the conductance part and the ones we have previously found out that is these are for what? therefore, admittance.

02:44 Alright.

02:45 So this is the part for the answers of the admittance.

02:48 Alright.

02:49 And now we will go to the last part of the party of the problem.

02:54 Here we will find out what? here we will find out the susceptance.

02:59 Alright.

02:59 So, so it is equal to what? it is equal to 1 divided by reactance.

03:05 Alright.

03:07 And it is denoted by what? p.

03:09 Alright...