Apply the rules for series and parallel circuits to current, voltage and total resistance, and analyze simple circuits to find the current through and voltage across each component.

What this topic is asking

This dot point applies Ohm's law to whole circuits by giving the rules for series and parallel connections. The Physical Setting/Physics course asks you to know how current, voltage and total resistance behave in each arrangement, to calculate the equivalent resistance, and to analyze a simple circuit to find the current through and voltage across each component. The Regents tests circuit analysis heavily, including reading circuit diagrams with their standard symbols.

Series circuits

In a series string (like old fairy lights), the same current flows through each bulb, and each bulb takes a share of the voltage set by its resistance. Because resistances add, the total is always greater than the largest single resistor. A break anywhere in a series circuit stops the current everywhere, since there is only one path.

Parallel circuits

Household wiring is parallel, so every appliance gets the full mains voltage and can be switched independently: a break in one branch does not stop the others. The reciprocal rule for parallel resistance is the most error-prone calculation in the module, because students forget to invert the final sum back to get $R_{total}$.

Analyzing a circuit

The general approach: find the equivalent resistance using the series or parallel rule, then use Ohm's law ($I = \dfrac{V}{R}$) with the source voltage to find the total current. From there, apply the series rules (same current) or parallel rules (same voltage) to find the current through and voltage across each component. Keeping a clear record of which quantity is shared (current in series, voltage in parallel) is the key to not getting lost.

Reference Tables note

The Reference Tables summarize the series and parallel rules (for current, voltage and resistance) alongside the circuit symbols for cells, resistors, switches, voltmeters and ammeters. Ohm's law ($R = V/I$) and the power equations are also printed and combine with these rules. You supply the strategy of reducing the circuit to an equivalent resistance, then working back through the components, and the care to invert the reciprocal sum in parallel.

Try this

Q1. State what is the same for every component in a series circuit, and what is the same for every branch in a parallel circuit. [2 points]

• Cue. Series: the current is the same. Parallel: the voltage is the same.

Q2. Two $4.0$ ohm resistors are connected in parallel. Calculate the equivalent resistance. [2 points]

• Cue. $\dfrac{1}{R_{total}} = \dfrac{1}{4.0} + \dfrac{1}{4.0} = \dfrac{2}{4.0}$, so $R_{total} = 2.0$ ohms (half of one resistor, as expected for two equal parallel resistors).