Circuit Elements and Ohm’s Law (4C) - MCAT Chemical and Physical Foundations of Biological Systems

Ampere (A); $1,\text{A} = 1,\text{C},\text{s}^{-1}$. Electric current measures the rate of charge flow, defined as one coulomb per second in SI units.

$E = Pt$. Electrical energy is the product of power and time for constant power dissipation.

$P = \frac{V^2}{R}$. Power in a resistor also derives from Ohm’s law, expressed as voltage squared divided by resistance.

$P = I^2R$. For resistors, power dissipation derives from combining Ohm’s law with the general power formula, using current squared times resistance.

$P = IV$. Electrical power is the rate of energy transfer, given by the product of current and voltage.

$P = 24,\text{W}$. Power dissipation is voltage squared divided by resistance.

Voltage $V$ is the same across each parallel branch. In parallel circuits, branches share the same potential difference due to common connection points.

$R_{\text{eq}} = R_1 + R_2 + \cdots$. In series, resistances add because the same current flows through each, accumulating opposition.

It has constant $R$; $I \propto V$ (linear $I$-$V$ curve). An ohmic device obeys Ohm’s law with constant resistance, yielding a linear current-voltage relationship.

$V = IR$. Ohm’s law states that potential difference is directly proportional to current, with resistance as the proportionality constant.

$P = 36,\text{W}$. Power dissipation uses current squared multiplied by resistance.

Volt (V); $1,\text{V} = 1,\text{J},\text{C}^{-1}$. Voltage represents the potential energy difference per unit charge, equivalent to one joule per coulomb.

Ohm ($\Omega$); $1,\Omega = 1,\text{V},\text{A}^{-1}$. Resistance quantifies opposition to current flow, defined as one volt per ampere.

$\sum I_{\text{in}} = \sum I_{\text{out}}$. Kirchhoff’s current law enforces charge conservation at a node, balancing incoming and outgoing currents.

$\sum \Delta V = 0$ around any closed loop. Kirchhoff’s voltage law upholds energy conservation, summing potential differences to zero in a closed loop.

$R = \rho\frac{L}{A}$. Resistance scales with material resistivity and length while inversely with cross-sectional area.

$R$ doubles: $R \propto L$. Resistance is directly proportional to length, so doubling length doubles resistance.

$R$ halves: $R \propto \frac{1}{A}$. Resistance is inversely proportional to cross-sectional area, so doubling area halves resistance.

$I = 4,\text{A}$. Ohm’s law gives current as voltage divided by resistance.

$V = 10,\text{V}$. Ohm’s law calculates voltage as current multiplied by resistance.

$R_{\text{eq}} = 5,\Omega$. Equivalent resistance in series is the sum of individual resistances.

$R_{\text{eq}} = \frac{6}{5},\Omega$. Equivalent resistance in parallel is the reciprocal of the sum of reciprocals.

$R_{\text{eq}} = \frac{R}{3}$. For identical parallel resistors, equivalent resistance equals individual resistance divided by the number.

Current $I$ is the same through each series element. In series circuits, conservation of charge ensures identical current through all elements.