Question

A $750Hz,20V$ source is connected to a resistance of $100\Omega$, an inductance of $0.1803H$ and a capacitance of $10\mu F$, all in series. The time in which the resistance (thermal capacity $=2J{/}^{0}C$) will get heated by ${10}^{0}C$ is

• A. 348 s
• B. 328 s
• C. 248 s
• D. 228 s

Answer 1

Answer: (A)

348 s

$\omega =2\Pi \times 750$

$=1500\Pi$

$R=100\Omega ,L=0.1803H,C=10\mu F$

$z=\sqrt{{100}^2+(\omega L-\frac{1}{\omega c}{)}^2}$

$z=834\Omega$

$Irms=\frac{20}{834}=0.024A$

$Paug=0.024\times 20\times \frac{100}{834}=0.0583/s$

total heat required $=10\times 2=\left(0.058\right)-\left(\Delta t\right)$

$\Delta t=348s$