Question 3
[Marks 14]
(i) Two light bulbs of resistance $R_A = 1 \Omega$ and $R_B = 5 \Omega$ are connected (a) in parallel and (b) in series.
Derive the expression of power dissipation and show which one will glow brighter in either
configuration, taking the power source to be $\varepsilon$ (V).
[4]
(ii) State Kirchoff's rules for electrical circuit analysis.
[2]
(iii) In the following circuit there are two power sources $V_1$, $V_2$ and three resistors $R_1$, $R_2$ and $R_3$. The
directions of currents $I_1$, $I_2$ and $I_3$ are considered initially in order to solve this circuit.
$I_1$
$I_2$
$I_3$
$V_1$
$R_2$
$R_3$
$V_2$
$R_1$
(a) Apply Kirchhoff's rules to determine an expression for $I_3$ in terms of $V_1$, $V_2$ and three resistors
$R_1$, $R_2$ and $R_3$ only.
[4]
(b) Determine the sign and the values of $I_1$, $I_2$ and $I_3$ for $V_1 = 10 \text{ V}$, $V_2 = 3 \text{ V}$; $R_1 = 5 \Omega$, $R_2 = 10 \Omega$,
and $R_3 = 15 \Omega$.
[4]
