Two currents are represented by I1= 15 sin (wt + π/3) and I2= 25 sin (wt + π/4). These currents are fed into common conductor. Find the total current. If the conductor has resistance 500hms, what will be energy loss in 10 hours? -

Given: I1 = 15 sin (wt + π/3)

I2 = 25 sin (wt + π/4)

R= 50 Ω

t= 10 hours = 360000s

Writing I1 and I2 in phase form,

I1 = 15/\/2 < $\bar{60}o$ = 10.61< 60o

I2 = 25/\/2 < $\bar{45}o$ = 17.68 < 45 o

∴ Total current= I = I1 +I2

= 10.61 < 60o + 17.68o < 45o

∴ Total current, I = I1 + I2

= 10.61 <60o + 17.68o< 45o

= 28.06 < 50.62o

= 39.68 sin (wt + 50.62o)

∴ I = 28.06 \/2 sin (wt + 50.62o)

= 39.68 sin (wt + 50.62o)

∴ Energy cos sin 24 hours,

E= I2R2 (Irms)

∴ E= (28.06) o * 50 * 36000 = 1.417 J