17.5 Parallel resistors
End of chapter exercises
Interactive Exercises
Exercise 17.9
Presentation: VPftf
The potential difference across the terminals of a battery when it is not in a complete circuit is the electromotive force (emf) measured in volts (\(\text{V}\)).
The potential difference across the terminals of a battery when it is in a complete circuit is the terminal potential difference measured in volts (\(\text{V}\)).
Voltage is a measure of required/done to move a certain amount of charge and is equivalent to \(\text{J·C$^{-1}$}\).
Current is the rate at which charge moves/flows and is measured in amperes (A) which is equivalent to \(\text{C·s$^{-1}$}\).
Conventional current flows from the positive terminal of a battery, through a circuit, to the negative terminal.
Ammeters measure current and must be connected in series.
Voltmeters measure potential difference (voltage) and must be connected in parallel.
Resistance is a measure of how much work must be done for charge to flow through a circuit element and is measured in ohms (\(\text{Ω}\)) and is equivalent to \(\text{V·A$^{-1}$}\).
Resistance of circuit elements is related to the material from which they are made as well as the physical characteristics of length and cross-sectional area.
Current is constant through resistors in series and they are called voltage dividers as the sum of the voltages is equal to the voltage across the entire set of resistors.
The total resistance of resistors in series is the sum of the individual resistances, \({R}_{S}={R}_{1}+{R}_{2}+\ldots\)
Voltage is constant across resistors in parallel and they are called current divides because the sum of the current through each is the same as the total current through the circuit configuration.
The total resistance of resistors in parallel is calculated by using \(\frac{1}{{R}_{P}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+ \ldots\) which is \({R}_{P}=\frac{{R}_{1}{R}_{2}}{{R}_{1}+{R}_{2}}\) for two parallel resistors.
Physical Quantities
Unit symbol
Potential difference (\(\text{V}\))
\(\text{V}\)
Voltage (\(\text{V}\))
Current (\(\text{I}\))
\(\text{A}\)
Resistance (\(\text{R}\))
\(\text{Ω}\)
Table 17.1: Units used in electric circuits
temp text
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