Circuit analysis and magnetism concepts and equations relevant to the MCAT physical sciences section. Front: the term or equation. Back: definition or equation with a brief usage note.
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- Ohm's Law (equation)
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V = IR; voltage across a resistor equals current times resistance.- Resistance of a wire (resistivity equation)
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R = (rho x L) / A; resistance increases with length and resistivity, decreases with cross-sectional area.- Electric power in a circuit (basic formula)
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P = IV; power equals current times voltage.- Electric power in terms of current and resistance
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P = I^2 R; useful when voltage is unknown but current and resistance are known.- Electric power in terms of voltage and resistance
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P = V^2 / R; useful when current is unknown but voltage and resistance are known.- Total resistance of resistors in series
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R_total = R1 + R2 + R3 + ...; series resistances simply add.- Total resistance of resistors in parallel
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1/R_total = 1/R1 + 1/R2 + 1/R3 + ...; parallel total resistance is always less than the smallest individual resistor.- Capacitance (definition)
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C = Q/V; capacitance is the ratio of stored charge to voltage across a capacitor.- Total capacitance of capacitors in parallel
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C_total = C1 + C2 + C3 + ...; parallel capacitances simply add.- Total capacitance of capacitors in series
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1/C_total = 1/C1 + 1/C2 + 1/C3 + ...; series total capacitance is always less than the smallest individual capacitor.- Energy stored in a charged capacitor
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U = 1/2 C V^2; energy stored depends on capacitance and the square of the voltage.- Kirchhoff's Current Law (junction rule)
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The sum of currents entering a junction equals the sum of currents leaving it; charge is conserved at every node.- Kirchhoff's Voltage Law (loop rule)
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The sum of voltage changes around any closed loop in a circuit equals zero; energy is conserved around a loop.- RC circuit time constant
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tau = RC; the time for a charging or discharging capacitor's voltage to change by about 63 percent toward its final value.- Terminal voltage of a battery with internal resistance
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V_terminal = EMF - I r; terminal voltage is less than EMF because of the voltage drop across internal resistance r.
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