Question 15 Marks

As shown in the figure above $A$ and $B$ are two lamps. Lamp $A$ is rated at $12\ V, 24\ W.$ Lamp $B$ is rated at $6.0 \ V.$ When lamp $B$ operates at its rated voltage, the current in it is $3.0 \ A$. The values of $R_1$ and $R_2$ are chosen so that both lamps operate at their rated voltages.
Based on the information given, answer the following.
$(i)$ Calculate the current in Lamp $A$.
$(ii)$ State and give reason for the reading of the Voltmeter.
$(iii)$ Calculate the resistance of $R_2$.
$(iv)$ Find the value of the resistance $R_1$.
Answer
View full question & answer→$(i)$ Use of $P = IV (0.5)$
$I = P \div V =24\ W \div 12 V$
Current in lamp $A - 2 A (0.5)$
$(ii)$ Voltmeter reading $= 12\ V (0.5)$
Lamp $A$ and Lamp $B$ are in parallel.
Hence $p.d$. across the arm containing $A = p.d.$ across arm
containing $B$
$= 12\ V ($from a$)$
$(iii)\ p.d.$ across $R_2 = 12\ V - 6\ V = 6\ V (0.5)$
$p.d.$ across $B = 6\ V ($given$)$
Hence$ p.d$. across $R_2 = 12\ V - 6\ V = 6\ V$
Current through $R_2$ = Current through $B = 3A ($given$) (0.5)$
Use of $R = V/I$
$R_2=6V/3A = 2\Omega$
$(iv)$ Current through $R_1 =$ Total Current $= 3A+2A = 5A (0.5)$
$p.d.$ across $R_1 = 15V - 12 V = 3V$
$R_1 = 3V/5A = 0.6 \ \Omega\ (0.5)$
$I = P \div V =24\ W \div 12 V$
Current in lamp $A - 2 A (0.5)$
$(ii)$ Voltmeter reading $= 12\ V (0.5)$
Lamp $A$ and Lamp $B$ are in parallel.
Hence $p.d$. across the arm containing $A = p.d.$ across arm
containing $B$
$= 12\ V ($from a$)$
$(iii)\ p.d.$ across $R_2 = 12\ V - 6\ V = 6\ V (0.5)$
$p.d.$ across $B = 6\ V ($given$)$
Hence$ p.d$. across $R_2 = 12\ V - 6\ V = 6\ V$
Current through $R_2$ = Current through $B = 3A ($given$) (0.5)$
Use of $R = V/I$
$R_2=6V/3A = 2\Omega$
$(iv)$ Current through $R_1 =$ Total Current $= 3A+2A = 5A (0.5)$
$p.d.$ across $R_1 = 15V - 12 V = 3V$
$R_1 = 3V/5A = 0.6 \ \Omega\ (0.5)$





