CAIE A-Level Physics AS 10.2.3 Kirchhoffs Laws a Formula for the Combined Resistance of Two or More Questions

Practise deriving series and parallel resistance relationships from Kirchhoff’s laws by tracking current and potential differences in the network.

Exam points

derive the equivalent resistance of resistors in series from Kirchhoff’s laws
show how current and potential differences combine in a series network to obtain the formula

[Maximum number: 2]

A cell with internal resistance r is connected to two resistors of resistances $R_{1}$ and $R_{2}$ as shown in Fig. 6.1.

Fig. 6.1

The potential differences (p.d.s) across $R_{1}$ and $R_{2}$ are $V_{1}$ and $V_{2}$ respectively.
The terminal p.d. across the cell is V.
The current in the circuit is I.

Use Kirchhoff's laws to show that the total resistance $R_{\mathrm{T}}$ of the external circuit is given by

R_{\mathrm{T}}=R_{1}+R_{2} .

(by Kirchhoff's second law) $V=V_{1}+V_{2}$
so $I R_{\mathrm{T}}=I R_{1}+I R_{2}($ and cancelling I gives $) R_{\mathrm{T}}=R_{1}+R_{2}$

or

$V / I=V_{1} / I+V_{2} / I$ (and substituting R gives) $R_{\mathrm{T}}=R_{1}+R_{2}$

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CAIE A-Level Physics AS 10.2.3 Kirchhoffs Laws a Formula for the Combined Resistance of Two or More Questions question 1