13
Problem solving
Textbook: pp. 45–46
GoalSolve problems on charge, work, voltage and number of electrons using q = It and A = qU together.
New words
amount of charge · zaryad miqdoriwork of the source · manbaning ishinumber of electrons · elektronlar soniconverting time to seconds · vaqtni sekundga o‘tkazish
Explanation
Problems in this topic use two formulas one after another: first the charge is found from current and time, q = I·t, then the work from charge and voltage, A = q·U. Time must be in seconds: 1 min = 60 s, 1 h = 3600 s; a current in mA is changed to amperes. To find the number of electrons, divide the charge by the charge of one electron, N = q/e, with e = 1.6·10⁻¹⁹ C. Checking units helps: A·s = C, C·V = J. Always write the unit in the answer. Before solving, draw a sketch and mark which quantities are given.
Worked examples
A device carries 50 mA for 10 min at 4 V. q = I·t = 0.05 · 600 = 30 C; the work is A = q·U = 30 · 4 = 120 J.
A current of 0.32 A flows through a lamp for 5 min: q = 0.32 · 300 = 96 C. The number of electrons is N = 96 : 1.6·10⁻¹⁹ = 6·10²⁰.
Class activity
Set out a model “two-stage problem” in your notebook: 1) givens and conversion to SI; 2) q = It; 3) A = qU; 4) answer. Solve one with numbers of your own and compare with a classmate’s solution.
Practice
1
A current of 0.15 A flows through a lamp for 4 min. How many coulombs pass?
36
2
An accumulator stores 7200 C of charge. For how many minutes can it supply 3 A?
40
3
This accumulator is 12 V. How many joules of work does the source do when all its charge is moved?
86400
4
Why do we first use current and time to find q in A = qU, and why must time be in seconds?
The work depends on charge, and q = I·t; since an ampere is a coulomb per second, time must be in seconds.