25
Mixed connection of consumers (for self-study)
Textbook: pp. 75–76
GoalLearn to find the total resistance of a mixed circuit using an equivalent diagram.
New words
mixed connection · aralash ulanishequivalent diagram · ekvivalent sxemasplitting into parts · qismlarga ajratishtotal resistance · umumiy qarshilik
Explanation
A mixed connection has parts connected in series and parts connected in parallel. To solve such a circuit we simplify it step by step: first replace a parallel (or series) part by one equivalent resistance, then simplify the new, simpler diagram in the same way. For a parallel part we use R = R₁R₂/(R₁ + R₂), for a series part R = R₁ + R₂. Once the total resistance is found, Ohm’s law gives the total current, and then, working backwards, the voltage and current in each part. The book gives this topic for self-study, so be sure to draw the diagram step by step in your notebook.
Worked examples
R₁ = 10 Ω is in series with R₂ and R₃ (20 Ω each) connected in parallel. The parallel part: 20 : 2 = 10 Ω. Total R = 10 + 10 = 20 Ω. With U = 20 V, I = 20 : 20 = 1 A.
In this circuit U₁ = 1 · 10 = 10 V and the parallel part also has 10 V. I₂ = I₃ = 10 : 20 = 0.5 A; the sum 0.5 + 0.5 = 1 A equals the total current.
Class activity
Draw in your notebook a mixed circuit with 3 resistors and turn it into an equivalent diagram in two stages (draw a new diagram at each stage). Pencil and paper only.
Practice
1
How do we solve a mixed circuit?
We replace parts by equivalent resistances and simplify step by step.
2
4 Ω and 12 Ω in parallel, with 7 Ω in series with them. The total resistance in ohms?
10
3
If 30 V is applied to the circuit above, what is the total current in A?
3
4
Why do we find the total current first and only then the voltage on the parallel part?
The voltage on the parallel part is its equivalent resistance times the total current, so the current is needed first.