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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]

          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]

Question 3
[Marks 14]
(i) Two light bulbs of resistance RA = 1 Ω and RB = 5 Ω 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 ε (V).
[4]
(ii) State Kirchoff's rules for electrical circuit analysis.
[2]
(iii) In the following circuit there are two power sources V1, V2 and three resistors R1, R2 and R3. The
directions of currents I1, I2 and I3 are considered initially in order to solve this circuit.
I1
I2
I3
V1
R2
R3
V2
R1
(a) Apply Kirchhoff's rules to determine an expression for I3 in terms of V1, V2 and three resistors
R1, R2 and R3 only.
[4]
(b) Determine the sign and the values of I1, I2 and I3 for V1 = 10 V, V2 = 3 V; R1 = 5 Ω, R2 = 10 Ω,
and R3 = 15 Ω.
[4]

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