DC Circuits Workbook

Two free sample problems

Word for word from the book, with the worked solution.

Problem 35: A load on a divider

Two 10 kΩ resistors split 12 V. What is the output with no load? What is it with a 10 kΩ load connected, and by how much has it fallen?

Show the worked solution

1. Unloaded: 12 × 10 / 20 = 6 V.
2. The load is in parallel with R2: 10 kΩ ∥ 10 kΩ = 5 kΩ.
3. Loaded: 12 × 5 / (10 + 5) = 4 V.
4. Change: (4 − 6) / 6 = −33.3 %. A load as low as the divider’s own resistors pulls the output a long way down.

Answer: Unloaded: 6 V · Loaded: 4 V · Change: −33.3 %

Problem 84: Current in a bridge’s middle arm

Find the current in R5 using Thevenin’s theorem.

Show the worked solution

1. Take R5 out. The left side is a divider: VL = 12 × 2 / 3 = 8 V. The right side: VR = 12 × 1 / 3 = 4 V. Vth = 8 − 4 = 4 V, left side higher.
2. Sources to a wire. From the gap, R1 ∥ R2 = 0.667 kΩ and R3 ∥ R4 = 0.667 kΩ, in series: Rth = 1.33 kΩ.
3. Put R5 back: I5 = 4 / (1.33 + 1) = 1.71 mA, flowing left to right.

Answer: Vth: 4 V · Rth: 1.33 kΩ · I(R5): 1.71 mA

Who it is for

Students in class 11–12 physics, diploma and polytechnic electrical or electronics courses, ITI electrician and electronics mechanic trades, and first-year engineering, plus hobbyists who want to work out a circuit on paper before they build it. It starts at Ohm’s law and assumes nothing beyond basic algebra.

Everything in the pack is also free on the site, spread across these pages. The pack puts it on paper in one place:

• LED resistor calculator
• Voltage divider calculator
• Resistor colour code calculator

Tips and tricks

• Redraw the circuit before you calculate. Put the source on the left and the bottom rail at 0 V, and mark every node you need a voltage for. Most wrong answers start with a misread circuit.
• Write the unit at every step. Volts divided by kilohms gives milliamps, and milliamps times kilohms gives volts, so you can work in kΩ and mA and skip the powers of ten.
• Check that every answer makes sense. A parallel pair always comes out below its smaller resistor, a divider’s output always sits between 0 V and its input, and the currents into a node add to zero.
• Find voltages and currents first and power last. Powers do not add by superposition; problem 67 shows why.
• When your answer differs from the book in the last digit, look at your rounding before your method. Keep full precision until the final line.
• Solve the hard ones twice by different routes, say nodal analysis and Thevenin. Problems 42, 65 and 80 solve the same circuit three ways.

Questions

What level is it?

It starts with one-line Ohm’s law problems and ends with bridges and multi-source networks. Class 11–12 physics, diploma, ITI and first-year engineering students will find most of their DC syllabus in it. Each problem is marked warm-up, core, stretch or challenge.

Are the answers right?

Each figure is drawn from a circuit description that a nodal-analysis program also solved, and a printed answer had to match that solution at every digit shown. Where our calculators cover the same sum, such as LED resistors, dividers and bridges, their code was run too and had to agree.

Does it cover AC circuits?

No. This book is DC only: resistors, sources, LEDs as fixed forward voltages, batteries and meters. An AC workbook with RC, RL and RLC circuits is planned as a separate book.

Can I use it on a phone or tablet?

Yes. It is an ordinary PDF, and the figures are vector drawings that stay sharp when you zoom in. On a phone the A4 pages are small, so a tablet or a printout is easier to work from.

Can a teacher use it with a class?

The PDF is for one person’s study. For a classroom, coaching centre or ITI batch, write to [email protected]; an institute licence is planned.