← Theme B · Particulate Nature of Matter
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Theme B · Particulate Nature of Matter

Chapter 2 · Electric circuits

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Electric current
I=Qt  ⇔  Q=ItI = \frac{Q}{t}\;\Leftrightarrow\; Q = It
Rate of charge flow; amperes (A).
Voltage = energy/charge
V=WQ  ⇒  W=QV=VItV = \frac{W}{Q}\;\Rightarrow\; W = QV = VIt
Energy delivered; also W=PtW = Pt.
Ohm's law
V=IR    (R=V/I)V = IR\;\;(R = V/I)
Electrical power
P=VI=I2R=V2RP = VI = I^2R = \frac{V^2}{R}
Resistors in series
RT=R1+R2+⋯R_T = R_1 + R_2 + \cdots
Current SAME in each; voltages add (Vi=IRiV_i = IR_i).
Resistors in parallel
1RT=1R1+1R2+⋯\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots
Voltage SAME across each; currents add. Two: RT=R1R2R1+R2R_T=\tfrac{R_1R_2}{R_1+R_2}.
EMF & internal resistance
ε=I(R+r)\varepsilon = I(R + r)
Terminal voltage V=ε−IrV = \varepsilon - Ir.
1st law of thermodynamics
Q=ΔU+WQ = \Delta U + W
Energy conservation for a gas.
2nd law (entropy)
Total entropy never decreases; heat flows hot → cold spontaneously.
Carnot efficiency
ηmax⁡=1−TcoldThot\eta_{\max} = 1 - \frac{T_{cold}}{T_{hot}}
Temperatures in kelvin; no engine can beat this.
Charge & the coulomb
Q=ItQ = It
1 C = 1 A·s (charge when 1 A flows for 1 s). Electron charge e=1.6×10−19e = 1.6\times10^{-19} C.
Current direction
Conventional current: + → − in the external circuit. Real electrons flow the OPPOSITE way (− → +).
Inside a battery
Chemical energy does work to separate charge, maintaining the e.m.f. (energy per coulomb, V = J/C).
Battery symbol
Long thin bar = + terminal; short thick bar = − terminal.
Kirchhoff's laws
Junction: currents in = currents out. Loop: sum of e.m.f. = sum of IRIR drops (energy conservation).
Series vs parallel (why)
Series: same I, voltages add ⇒ R adds. Parallel: same V, currents add ⇒ total R < smallest branch.
Key SI units
II: A · QQ: C · VV, e.m.f.: V (= J C⁻¹) · RR: Ω · PP: W · WW: J.
Common traps
Confusing conventional current with electron flow; using kJ not J; forgetting internal resistance rr drops the terminal voltage.