Posted: October 24th, 2023

When the switch is connected to A, determine the frequency

Homework G:Due Friday April 18, 2014 at conferenceInstructions: Please provide a brief verbal explanation of each step in your solution. Statewhere the formulas are coming from, and why they are applicable here. Use symbols andformulae effectively defining their meaning and making it clear whether they are vectors orscalars. Write legibly, and draw large and clearly labeled sketches.Problem 1Consider the circuit in Fig. 1 containing a three-way switch. The switch can connect eitherto A or to B or can remain open. The voltage source supplies an alternating voltage withfixed amplitude V0 and frequency ω that can be varied.(a) When the switch is connected to A, determine the frequency at which the magnitudeof the current through the resister will be a maximum. What is the value of the currentin this case?(b) Imagine we hold the frequency at the value found in part (a) and connect the switchto B. What is the average power dissipated by the circuit?(c) Imagine we again hold the frequency at the value found in part (a) and move the switchto the open position. Find the value for the resistor R at which the magnitude of thecurrent will be one half the value found in part (a).Figure 1: switchable AC circuit.1Problem 2Consider the AC circuit shown in Fig. 2. The voltage source provides a time dependentvoltage of the form V (t) = V0 sin ωt.(a) Sketch a phasor diagram for voltages and currents in the circuit.(b) By analyzing your diagram, show the amplitude of the AC voltage over the inductorVL =V01 + R2 (ωC − (1/ωL))2(1)(c) Sketch VL versus ω and provide simple arguments for the values it assumes for ω → 0,√for ω → ∞, and for ω = 1/ LCFigure 2: Image of AC circuit.2Problem 3Consider the AC Power transmission system sketched in Fig. 3. The RMS generatorAC voltage is v1 = 110 V and the number of windings on the primary coil of the idealtransformer N1 = 500. The transmission line (between the transformers) is made of copperwire with a radius of 1 cm and has a total length of 50 km. The resistivity of copper isρ = 1.7 × 10−8 Ωm.(a) Determine the resistance of the transmission line.(b) There is a total power consumption of 200 kW by consumers. Determine the loadresistance RL .(c) Determine N2 and the voltage of the transmission line required to keep the transmissionlosses in RT below 10% of the power delivered to the load RL . Use that i1 v1 ≈ i2 v2across each transformer.(d) Determine the fraction of power delivered by the source that would go to the consumerif there were no transformers and the generator was connected to the load directly withthe copper transmission lines.Figure 3: Image of high voltage power delivery system.

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