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  4. A 110 V d.c. heater is used on an a.c. source, such that the heat produced is same as it produces when connected to 110 V dc in samel time-intervals. What would be the r.m.s. value of the altemating voltage?

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Q. A $110\,V$ d.c. heater is used on an a.c. source, such that the heat produced is same as it produces when connected to $110 \,V$ dc in samel time-intervals. What would be the r.m.s. value of the altemating voltage?

Alternating Current

Solution:

Given that $H_{A C}=H_{D C}$
$l_{\text{rms}}^{2} R t=l^{2} R t$
$\frac{V_{\text{rms}}^{2}}{R}=\frac{V^{2}}{R}$
$V_{\text{rms}}= V$
so $V_{\text{rms}}=110\, V$