Lessons 21–22 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, J.E. Usarov, K.T. Suyarov, M.K. Yuldasheva. Physics, textbook for Grade 8 of general secondary schools, revised and enlarged 3rd edition. “O‘qituvchi” Publishing and Printing Creative House, Tashkent, 2019
22
Connecting consumers in parallel
Textbook: pp. 67–70
GoalKnow the laws of voltage, current and resistance for conductors connected in parallel and apply them in problems.
New words
parallel connection · parallel ulanishbranching point · tarmoqlanish nuqtasisum of currents · tok kuchlari yig‘indisihousehold devices · uy-ro‘zg‘or asboblari
Explanation
In a parallel connection the beginnings of the conductors are joined at one point and the ends at another, so the circuit branches. The voltage is the same on every branch: U = U₁ = U₂. The total current equals the sum of the branch currents: I = I₁ + I₂. For the total resistance 1/R = 1/R₁ + 1/R₂; for two conductors R = R₁·R₂/(R₁ + R₂), so the total resistance is smaller than even the smallest branch. For n equal conductors R = R₁/n. Household devices are connected in parallel: each gets the same voltage, and switching one off leaves the others working. Plugging many devices into one socket raises the current and heats the wire, so adults must watch for this.
Worked examples
R₁ = 30 Ω and R₂ = 60 Ω in parallel: R = 30 · 60 : (30 + 60) = 1800 : 90 = 20 Ω.
If U = 12 V is applied: I₁ = 12 : 30 = 0.4 A, I₂ = 12 : 60 = 0.2 A, I = 0.4 + 0.2 = 0.6 A. Check: 12 : 20 = 0.6 A.
Class activity
Draw in your notebook the diagram of two resistors in parallel, mark the branching points and show the current direction in each branch with arrows.
Practice
1
Which equalities hold for voltage and current in a parallel connection?
The voltage is the same on all branches; the total current is the sum of the branch currents.
2
What is the total resistance in ohms of 30 Ω and 70 Ω resistors in parallel?
21
3
Four identical 12 Ω resistors are connected in parallel. What is the total resistance in ohms?
3
4
Why are household devices connected in parallel rather than in series?
Each device gets the full voltage and switching one off leaves the others working.