Chapter 1 Practice Problems — Electric Charge and Basic Quantities
These problems are meant to build your problem-solving intuition. A hint is provided for each — try the problem on your own first before reading it.
Problem 1 — Charge and Current
A wire carries a steady current of 250 mA for 4 minutes.
(a) How much charge (in coulombs) passes through a cross-section of the wire during that time?
(b) How many electrons does this charge represent? (Recall: one electron carries \(-1.602 \times 10^{-19}\) C.)
(c) A second wire carries a current of 1.8 A. How long (in seconds) does it take for 540 mC to pass through?
Hint
(a) For a constant current, the charge is \(Q = I \cdot t\). Convert minutes to seconds first and milliamps to amps: 250 mA = 0.25 A, 4 min = 240 s.
(b) Each electron has a magnitude of charge \(e = 1.602 \times 10^{-19}\) C. The number of electrons is \(n = Q / e\). Your answer will be a very large number — on the order of \(10^{21}\).
(c) Rearrange \(Q = It\) to get \(t = Q/I\). Convert mC to C: 540 mC = 0.540 C.
Problem 2 — Voltage, Energy, and Power
A 9 V battery pushes 2 mA through a resistor.
(a) How much energy (in joules) is delivered to the resistor in 30 seconds?
(b) What is the power dissipated by the resistor?
(c) The resistor is now replaced with one that draws 50 mA from the same 9 V source. What is the new power dissipation? Express your answer in milliwatts.
Hint
(a) Use \(W = P \cdot t\), where \(P = V \cdot I\). Compute power first, then multiply by time.
(b) You already computed \(P = V \cdot I\) in part (a). Express it in milliwatts if the number is small.
(c) Apply the same formula with the new current. Compare your answers for parts (b) and (c) — the power grows rapidly with current.
Problem 3 — Ohm's Law and Power Forms
A resistor connected to a 5 V source dissipates 125 mW.
(a) Use \(P = V^2/R\) to find the resistance.
(b) What current flows through the resistor? (Use Ohm's Law.)
(c) Verify your power answer using \(P = I^2 R\).
Hint
(a) Rearrange \(P = V^2 / R\) to \(R = V^2 / P\). Substitute V = 5 V and P = 0.125 W. Keep units consistent.
(b) With R known, apply \(I = V/R\). Express in milliamps (mA) since the current will be small.
(c) Substitute your values of I and R into \(P = I^2 R\). The result should match 125 mW exactly, which serves as a self-check.
Problem 4 — Unit Conversions and SI Prefixes
Answer each unit-conversion question independently.
(a) A current of 3,500 μA is expressed in milliamps and in amps. Give both.
(b) A resistor is labeled 4.7 kΩ. A 15 V source is connected across it. Find the current in mA, using Ohm's Law.
(c) A sensor draws 820 nA from a 3.3 V supply. Calculate the power in picowatts (pW).
Hint
(a) Recall that \(1 \text{ mA} = 1000 \text{ μA}\) and \(1 \text{ A} = 10^6 \text{ μA}\). Divide 3,500 by 1000 to get mA, and by \(10^6\) to get A.
(b) Convert kΩ to Ω first: \(4.7 \text{ kΩ} = 4700 \text{ Ω}\). Apply \(I = V/R\), then convert A to mA by multiplying by 1000.
(c) Use \(P = V \cdot I\) with V = 3.3 V and I = \(820 \times 10^{-9}\) A. The result is in watts — convert to pW by multiplying by \(10^{12}\).