Question 221: AC fundamentals

Question

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $$\mu$$F and a resistance of 120 $$\Omega$$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/$$^\circ$$C will get heated by 16$$^\circ$$C is _____________ s.

Accepted Answer

L = 100 $$	imes$$ 10
$$-$$3
H
C = 100 $$	imes$$ 10
$$-$$6
F
R = 120 $$\Omega$$
$$\omega$$L = 10 $$\Omega$$
$${1 \over {\omega C}} = {1 \over {{{10}^4} 	imes {{10}^{ - 6}}}} = 100\,\Omega $$
$$\Rightarrow$$ X
C
$$-$$ X
L
= 90 $$\Omega$$
$$ \Rightarrow Z = \sqrt {{{90}^2} + {{120}^2}}  = 150\,\Omega $$
$$ \Rightarrow {I_{rms}} = {{20} \over {150}} = {2 \over {15}}A$$
For heat resistance by 16$$^\circ$$C heat required = 32 J
$$ \Rightarrow {\left( {{2 \over {15}}} ight)^2} 	imes (120) 	imes t = 32$$
$$t = {{32 	imes 15 	imes 15} \over {4 	imes 120}} = 15$$

AC fundamentals

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\muF and a resistance of 120 \Omega as shown in figure. The time in which the resistance having a thermal capacity 2 J/^\circC will get heated by 16^\circ$C is _____________ s.

Integer / Numeric Answer Type