A 110 , V d.c. heater is used on an a.c. sour | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The heat produced by a heater in a resistance $R$ over time $t$ is given by $H = \frac{V^2}{R} t$.For $d.c.$ voltage,$H_{dc} = \frac{V_{dc}^2}{R}

Vedclass · Accepted Answer

$110$

Vedclass · Answer

(A) The heat produced by a heater in a resistance $R$ over time $t$ is given by $H = \frac{V^2}{R} t$.For $d.c.$ voltage,$H_{dc} = \frac{V_{dc}^2}{R} t$.For $a.c.$ voltage,the heat produced is determined by the $r.m.s.$ value of the voltage,$H_{ac} = \frac{V_{rms}^2}{R} t$.Given that the heat produced is the same in both cases $(H_{ac} = H_{dc})$,we have:$\frac{V_{rms}^2}{R} t = \frac{V_{dc}^2}{R} t$$V_{rms}^2 = V_{dc}^2$$V_{rms} = V_{dc}$Given $V_{dc} = 110 \, V$,therefore $V_{rms} = 110 \, V$.

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

Similar Questions

The $ rms $ value of current in a $ 50 \,Hz $ $ AC $ circuit is $ 6 \,A $. The average value of $ AC $ current over a complete cycle is:

An alternating current is represented by the equation,$i = 100 \sqrt{2} \sin(100 \pi t) \ A$. The $\text{RMS}$ value of current and the frequency of the given alternating current are:

In an $AC$ circuit,when an $AC$ ammeter is connected,it reads $i$ current. If a student uses a $DC$ ammeter in place of the $AC$ ammeter,the reading in the $DC$ ammeter will be:

$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

$A$ current in a circuit is given by $i = 3 + 4 \sin \omega t$. The effective value of the current is

Vedclass Test Series

Exam Paper Generator

Online Exam Module