Electric Circuits and Capacitors

Electric Circuits and Capacitors: this Effortless Math guide explains the topic in plain language, shows how it works through solved examples, and gives you free practice to try immediately, so the idea sticks instead of staying abstract.

A circuit works only when charge has a closed path. Voltage supplies energy per charge, current measures charge flow, and resistance limits that flow.

This lesson supports Chapter 17 of High School Physics.

Ohm’s law connects voltage, current, and resistance

For an ohmic device, [V=IR.] Average current is (I_{text{avg}}=frac{Delta Q}{Delta t}). Resistance is measured in ohms. Electric power can be written (P=IV), (P=I^2R), or (P=frac{V^2}{R}), with the form chosen to match the known quantities.

Series and parallel circuits follow different rules

Series elements carry the same current, and their voltage drops add. Their equivalent resistance is (R_{text{eq}}=R_1+R_2+cdots). Parallel branches share the same voltage, and their currents add. Adding a parallel path lowers the equivalent resistance.

A capacitor stores separated charge and energy

Capacitance is (C=frac QV). A capacitor stores energy (U=tfrac12CV^2). In a direct-current circuit, a capacitor draws current while charging. After a long time in a simple steady circuit, it behaves like an open path.

Worked example

Two resistors, (4Omega) and (6Omega), are in series across (20text{ V}). Their equivalent resistance is (10Omega), so the current is (I=frac VR=frac{20}{10}=2text{ A}).

Watch the idea in action

The Organic Chemistry Tutor gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. Write Ohm’s law.
2. What does electric current measure?
3. How do series resistances combine?
4. What quantity is the same across parallel branches?
5. Define capacitance.
6. Write one formula for electric power.

Answers

1. (V=IR).
2. Charge flow per unit time.
3. They add.
4. Voltage.
5. (C=frac QV).
6. For example, (P=IV).

Keep studying

High School Physics includes 12 full-length practice tests: two in the book and ten online.

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