Question

The resistance of hot turngsten filament is about $10$ times the cold resistance. What will be the resistance of $100W$ and $200V$ lamp when not in use

• A. $40\Omega$
• B. $20\Omega$
• C. $400\Omega$
• D. $200\Omega$

Answer 1

The correct option is A $40\Omega$

Given,

$P=100W$

$V=200V$

$R_{hot}=10\cdot R_{cold}$

We know,

$P=I\cdot V$

$\to P=\frac{V}{R}\cdot V=V^2\cdot R$

$\therefore R=\frac{V^2}{P}$

where,

$P=$ Power

$I=$ Current

$R=$ Resistance

$V=$ Voltage

$R_{hot}=$ Hot Resistance

$R_{cold}=$ Cold Resistance

So, $R_{hot}=\frac{200\cdot 200}{100}=400\Omega$

$R_{cold}=\frac{R_{hot}}{10}=\frac{400}{10}=40\Omega$

$\Rightarrow R_{cold}=40\Omega$

$40\Omega$ will be the resistance of $100W$ and $200V$ lamp when not in use.