26
Problem solving
Textbook: pp. 76–78
GoalSolve problems on mixed circuits and check the results.
New words
current distribution · tok taqsimotivoltage distribution · kuchlanish taqsimotichecking · tekshirishequivalent resistance · ekvivalent qarshilik
Explanation
Before solving, draw the diagram and mark every resistor and the known quantities. Then find the equivalent resistance and use Ohm’s law for the total current. Next work backwards: using that the current is the same in series parts and the voltage is the same in parallel parts, find the current and voltage of each resistor. To check, see that the voltages add up to the source voltage and that the currents of parallel branches add up to the total current. If an equality fails, there is usually a mistake in the calculation or in reading the diagram.
Worked examples
R₁ = 4 Ω and R₂ = 12 Ω in parallel, R₃ = 7 Ω in series, U = 30 V. The parallel part is 4 · 12 : 16 = 3 Ω, R = 3 + 7 = 10 Ω, I = 30 : 10 = 3 A. U₃ = 3 · 7 = 21 V; the parallel part has 30 − 21 = 9 V.
Continued: I₁ = 9 : 4 = 2.25 A, I₂ = 9 : 12 = 0.75 A. Check: 2.25 + 0.75 = 3 A, equal to the total current.
Class activity
Play “problem detective”: a classmate solves a circuit with one deliberate mistake (for example a wrongly added resistance) and you find it. Notebook only.
Practice
1
Name two ways to check the solution of a mixed circuit.
The voltages must add up to the source voltage, and the parallel currents to the total current.
2
R₁ = 12 Ω and R₂ = 4 Ω are in series and this whole group is in parallel with R₃ = 16 Ω. What is the total resistance in ohms?
8
3
With 16 V applied to that circuit, what current in A flows through R₃?
1
4
Why is the current larger in the branch of smaller resistance?
The voltage is the same and I = U/R, so a smaller R gives a larger I.