Answer to Question #149093 in Electric Circuits for M.TARUN

Question

Three identical coils, each of resistance 15 Ω and inductance 42 mH are
connected (a) in star and (b) in delta to a 415 V, 50 Hz, 3-phase supply.
Determine the total power dissipated in each case.

Answer 1

We have given:

there are three resistors and their each values are R=15om,

and inductance is 0.042H,

line voltage V_L=415V,

frequency f=50Hz.

a)

Let`s find power in star connection.

X_L=$2\times \pi\times 0.042\times 50$=13.19,

then total resistance Z=R+jX_L,

Z=$\sqrt{\smash[b]{R^2+X^2}}$ = 19.97 om. Then we find total voltage and current:

V=$\frac{V(L)}{\sqrt{\smash[b]{3}}}$ =239.6v,

I=$\frac{V}{Z}$ =12 A. Then we can calculate dissipated power easily in star connection:

P=$3\times V\times I$ =8.625 kw. this is dissipated power in star connection.

b)

Let`s find power in delta connection.

Z is the same with in star connection,

V=V_L=415v,

I=$\frac{V}{Z}$=20.78 A, then

P=$3\times V\times I$ =25.871 kw this is dissipated power in delta connection.