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LearnCambridge97022025–2027Paper 2 · AS Level Structured QuestionsD.C. circuits

Paper 2 · Module

D.C. circuits

3 subtopics≈ 110 min in total

Start the module: E.m.f. and internal resistance Open graphing calculator

E.m.f. and internal resistance
A real source has an e.m.f. $E$ and an internal resistance $r$ . When it drives a current $I$ through an external resistance $R$ , some energy is dissipated inside the source: $E=I(R+r)$ , so the terminal p.d. is $V=E-Ir$ . The "lost volts" $Ir$ grow with current. A graph of $V$ against $I$ is a straight line with intercept $E$ and gradient $-r$ .
≈ 35 min
Kirchhoff's laws
Kirchhoff's first law: the sum of currents into a junction equals the sum out (conservation of charge). Kirchhoff's second law: round any closed loop, the sum of e.m.f.s equals the sum of p.d.s (conservation of energy). From these: series $R=R_1+R_2+\dots$ ; parallel $\dfrac1R=\dfrac1{R_1}+\dfrac1{R_2}+\dots$ .
≈ 40 min
Potential dividers
Two resistors in series share the supply p.d. in proportion to their resistances: $V_{\text{out}}=\dfrac{R_2}{R_1+R_2}V_{\text{in}}$ . Replacing one resistor with a thermistor or LDR makes the output depend on temperature or light. A potentiometer is a uniform resistance wire whose p.d. per unit length lets you compare e.m.f.s by finding the balance length, where a galvanometer reads zero.
≈ 35 min