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## Homework Statement

FIGURE 1 shows a 50 Ω load being fed from two voltage sources via

their associated reactances. Determine the current i flowing in the load by:

(a) applying Thévenin’s theorem

(b) applying the superposition theorem

(c) by transforming the two voltage sources and their associated

reactances into current sources (and thus form a pair of Norton

generators)

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## The Attempt at a Solution

(a)

Converting V1 & V2 to RMS values and V1 to a sin value:

V1 = 415sin(100πt+90)

V2 = 415sin(100πt)

and from Asin(ωt+Φ)

V1 = 415∠90V or 0+j415 V

V2 = 415∠0V or 415+j0 V

Then current around the circuit:

I =V/Z = (V2-V1) / (Z2+Z1) = (415-j415) / (j10)

This as a polar form division:

586.8986∠-45 / 10∠90 = 58.68986∠-135 A or -41.5-j41.5

Vt = V2 - Z2*I = 415+j0 - (0+j6)(-41.5-j41.5) = 415+j0-(-j249-249j^2) as j^2 = -1 then:

Vt = 415-(249-j249) = 166+j249V

ZL = 50@0.7lag = 50∠-45.572998 = 35+j35.70714Ω

Zt = j4in parallel with j6= j2.4

so load current:

I = V / ZL + Zt = 166+j249 / ( 0+j2.4 + 35+j35.70714 ) = 166+j249 / 35+j38.10714

this as a polar division I = 299.26∠56.310 / 51.741∠47.434 =

**5.784∠8.876A**

I have only completed part (a), once I know I'm on the right track I'll complete b & c. All help is greatly appreciated as always.

I have only completed part (a), once I know I'm on the right track I'll complete b & c. All help is greatly appreciated as always.