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ELEC1111 – Electrical Circuit Fundamentals

2021

QUESTION 1 [20 marks]

a. (10 marks) The circuit in Figure 1 is a diode-based protection circuit for a portable TV. The red LED will glow to indicate “FAULT — battery reversed” in case of wrong connection to a DC power supply (reversed polarity). With the correct polarity, the green LED will glow to indicate “OK — normal operation” .

The voltage drop across the 1N5400 diode and LEDs under forward bias is 2.1 volts. The TV is represented as a 200 Ω resistance.

i. (5 marks) Calculate the current through the TV and green LED when the circuit is in normal operation.

ii. (3 marks) Calculate the current through the red LED when the circuit is in FAULT mode.

iii. (2 marks) Describe how the 1N5400 diode can protect the TV when the polarity is reversed.

Figure 1

b. (10 marks) Find the Norton equivalent of the circuit shown in Figure 2 from terminals a-b.

Figure 2

QUESTION 2 [20 marks]

a. (8 marks) The flash unit of a camera is shown in Figure 3, where the flashlight is represented as a 12 Ω resistance. The capacitor is charged when the switch is at position

a. This charge then provides a burst of power to the flashlight when taking a picture, that is, when the switch is moved to position b.

i. (5 marks) Assume that the switch has been at position a for a long time. The switch is moved to position b to take a picture and the flash fires for 1.2 ms. Find the voltage v0 across the capacitor once the picture has been taken (at t=1.2 ms).

ii. (3 marks) Once the picture is taken at t=1.2 ms, the switch is moved back to position a. How long will it take for the capacitor to fully recharge before taking the next picture?

6 k

Figure 3

b. (12 marks) Switch 1 (SW1) in Figure 4 was in position a for a long time before moving to position b at t=0. After 0.1 seconds, the voltage source is disconnected from the circuit by opening Switch 2 (SW2).

i. (6 marks) Derive the expression for i0 (t) for 0 ≤ t < 0.1 s.

ii. (4 marks) Derive the expression for i0 (t) for t ≥ 0.1 s.

iii. (2 marks) Calculate the value of i0 at t = 0.2s.

SW1

t=0

QUESTION 3 [22 marks]

a. (10 marks) Resistance temperature detectors (RTDs), are sensors used to measure temperature based on the resistance changes. The most common type (PT100) has a resistance of 100 Ω at 0°C and 138.4 Ω at 100°C. The circuit shown in Figure 5 is used to convert the information from the RTD into something meaningful for an analog-to- digital converter (ADC).

i. (8 marks) Calculate the voltage v0 as a function of vin when the RTD has a value of 130 Ω .

ii. (2 marks) How large can be the value of vin before the amplifier saturates?

-5 V

100

Figure 5

b. (12 marks) Calculate the output voltage vo(t) in the circuit shown in Figure 6.

10 mF

QUESTION 4 [20 marks]

a. (8 marks) A regular household system of a single-phase three-wire circuit allows the operation of both 120 V and 240 V, 60 Hz appliances. The household circuit is shown in Figure 7. Calculate the current through each of the appliances (ilamp, iref and irange).

Figure 7

b. (12 marks) Calculate v0 (t) in the circuit of Figure 8.

Figure 8

QUESTION 5 [18 marks]

a. (9 marks) A coupling capacitor is used to block the DC current from an amplifier as shown in Figure 9(a). The amplifier and the capacitor act as the source, while the speaker is the load as in Figure 9(b).

i. (5 marks) Calculate the value of RL and the source frequency such that the circuit can deliver maximum average power to the speaker.

ii. (4 marks) If |Vin| = 4.6 VTmS, how much power is delivered to the speaker at that frequency?