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7.Alternating Current
medium
Calculate the capacitive reactance of a condenser in order to run a bulb rated at $10\,watt\, 60\,volt$ when connected in series to an $a.c.$ source of $100\,volt$........$\Omega $
A
$100$
B
$360$
C
$600$
D
$480$
Solution
$\mathrm{P}_{\mathrm{R}}=10 \mathrm{\,W} \quad \Rightarrow \mathrm{R}=\frac{\mathrm{V}^{2}}{\mathrm{P}}=\frac{(60)^{2}}{10}=360\, \Omega$
$\mathrm{V}_{\mathrm{R}}=60 \mathrm{\,V} \quad \mathrm{V}_{\mathrm{C}}^{2}+\mathrm{V}_{\mathrm{R}}^{2}=\mathrm{V}_{\mathrm{S}}^{2} \Rightarrow \mathrm{V}_{\mathrm{C}}=80 \mathrm{\,V}$
$I=\frac{V}{R}=\frac{60}{360}=\frac{1}{6}$
Applying Ohm's law for capacitor
$V_{C}=I X_{C}$
$X_{C}=\frac{80}{1 / 6}=480\, \Omega$
Standard 12
Physics
