EN.520.137: First Year ECE Design Homework 1

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EN.520.137: First Year ECE Design Homework 1

Total Points: 100

1. (10 points) Identify which of the elements in the following image are connected in:

(a) series

(b) parallel

(c) neither

2. (10 points) Resistors can often only handle dissipating 250 mW of power. Which of the follow-ing resistors may fail due to this power limit?

(a) A 50 Ω resistor with 40 mA flowing through it

(b) Connecting a 4.2 V fully charged lithium-ion battery to a 500 Ω resistor

(c) The voltage measured across the resistor is 14 V, and the current flowing through it is 400 µA.

(d) Two 100 Ω resistors are connected in parallel and connected to a 9 V battery’s terminals

(e) One 5 kΩ resistor is connected to the terminals of two AA batteries which are in series (approximately 3.6 V maximum)

3. (20 points) A ladder circuit (shown below) consists of resistors in series and parallel. What is the resistance of this infinitely long ladder circuit measured with respect to nodes A and D? Each resistor has resistance R.

You may assume the limit is finite. There are many ways to tackle this problem, ranging from starting with smaller circuits and looking for a pattern, to assuming that the resistance between

A and D is equivalent to the resistance between B and C with the resistor between B and C removed, using Kirchhoff’s Laws, etc.

4. (15 points) Reduce (simplify) the circuit below by combining all the resistances shown into a single resistor between the nodes A and B.

5. Assume you have a collection of 4 resistors with resistance values 120 Ω, 220 Ω, and 100 Ω. Then describe how each of the following resistances can be created by connecting those resistors together:

(a) (3 points) 320 Ω

(b) (3 points) 77.65 Ω

(c) (3 points) 274.55 Ω

(d) (3 points) 110 Ω

6. (20 points) Assume we have the following circuit, where the resistance of R5 is unknown.

Assuming the voltage across R3 is 20 V, what is the resistance of R5? Include 3 significant digits in your answer (so your intermediate values, if any, should have more in order to get the correct answer).

7. (13 points) Using the image below, the box in the circuit is a resistor whose value can be anywhere from 8 kΩ to 80 kΩ. Find the range of voltages on each end of the unknown resistor. You can do this by calculating the voltage at the two ends of the range of possible resistance values. Include 3 significant digits in your answer (so your intermediate values, if any, should have more in order to get the correct answer).