Question

A 20V, 750 Hz source is connected to a series combination of R $=$ 100$\Omega$, C $=$ 10 $\mu F$ and $L$=$0.1803H$. Calculate the time in which resistance will get heated by ${10}^o$C. (If thermal capacity of the material $=$ 2 J / ${}^o$C )

• A. 328 sec
• B. 348 sec
• C. 3.48 sec
• D. 4.32 sec

Answer 1

The correct option is B 348 sec

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

for heating by ${10}^{\circ }C,$ we need $={10}^{\circ }C\times 2J/C$

$=20J$ of heat

$z=\sqrt{{100}^2+{\left(2\pi \times 750\times 1803-\frac{1}{2\pi \times 750\times {10}^{-5}}\right)}^2}$

$z=834\Omega ,Irms=\frac{20}{834}=0.024A$

$Paug=VrmsIrmsCos\theta$

$=20\times 024\times \frac{100}{834}$

$=2\left(0.029\right)J/S=0.058J/s$

Total energy$=20=\left(t\right)Paug$

$20=t\times \left(0.029\right)\times 2$

$348sec=t$

all energy of the circuit is dissipated into resistor
one anerage there is no energy flow into capacitor or inductor