Unformatted text preview: 5(Isc + I/2) – 5(Isc – 5Ω I/2) = 0. Again, the terms involving I cancel out. Hence, Isc
5Ω = 1∠0° A, and ZTh =
10∠0 o
= 10 Ω. It follows that for
1∠0 o 10∠0° V + Isc + I/2 ISC – I/2
I I/2 j2 Ω
Isc – maximum power transfer, Z = 10
Ω. The power dissipated in the 1:2 2 ⎛V ⎞
1
load is ⎜ Th ⎟
⎜
⎟ 4 × 10 = 1.25 W.
⎝ 2⎠ 7/7 If the independent voltage source is replaced by a short circuit, the impedance on the
primary side is (5 + j10) Ω and ZTh = 4(5 + j10) = 20 + j40 Ω. j10 Ω 5Ω 3. Determine the
impedance seen
by the source, 4∠0° V assuming a = 2. 5Ω +
– j5 Ω Solution: Reflection
of the (5 – j5) Ω 1:a 2:1 through the RH transformer gives (20 – j20) Ω. The impedance on the secondary side of the
LH transformer is (25 – j10) Ω. Reflected to the primary side, this becomes (25 – j10)/a2 Ω. 4. If vsrc = 10cos(1,000t) V, determine the energy
stored in the circuit in the sinusoidal steady state
at t = 0, assuming C = 1 μF. 1H Solution: At t = 0, the voltage across C is 10 V and vsrc + C k = 0.5 – the current through the inductors is zero, being 1H proportional to the integral of vsrc. The energy stored
is W = 1
Cv 2 = 50C.
2
j5 Ω 5. Determine Rx given that I = 0
and R = 2 Ω. 8Ω Solution: Since I = 0, the voltage
across Rx is 10 V, and the same 30∠0 − 10∠0
current
R
o o flows +
j10 Ω – R I
Rx +
– 10∠0° V 6Ω
30∠0° V through R and Rx. It follows that
R R
20
R x = 10 , or R x = .
R
2 1:2
+ 7. Determine the maximum power that
can be delivered to RL, assuming R 2∠0° V –
5∠0° V = 0.5 Ω. +
– 1:2
RL Solution: The primary voltage of the upper transformer is always 1 V. On 3/5 open circuit, the source current is zero, the primary voltage is 5 – 1 = 4 V, and VTh = 8 V. On
short circuit, the primary voltage of the lower transformer is zero, the source current is (5 –
1)/R and the short circuit current is 2/R. This gives, RTh = 4R. The maximum power delivered
is (8)2/(4×4R) = 4/R.
RLine 8. Given that the load L consumes 1200 W at 0.8
p.f. lagging and the magnitude of the voltage
across L is 300 V rms. Determine the power
dissipated in the resistance Rline, if Rline = 0...
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 Spring '07
 RiadChedid
 Power, Power factor

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