Question

A heater wire whose power is $4\text{ }Kw$ is connected to $220\text{ }V$ source.
(A) Electric source calculate
(B) Resistance of heater
(C) Energy consumed in two hours

Answer 1

Hint: Use the formula of electric power, which is the product of voltage and current, from this by putting the value of power and voltage we get the value of current. Use ohm’s law to find the value of Resistance. To find the energy consumed in a specific time, we use the formula of electric energy.
Formula used: \[\text{Electric power}=\dfrac{\text{work done}}{\text{Time}}\]
If a current$I$ flows through a conductor of Resistance $R$ ohm for a time $t$ second under a potential difference $V$ volt, then electric power is given by $\dfrac{VIt}{t}$
                  $P=VI$
\[\begin{align}
  & \text{Ohm's law} \\
 & \text{ }V=IR \\
\end{align}\]
$\text{Electric energy}=\text{Power}\times \text{Time}$
Units: Power in watt, Resistance in ohm, Current in Ampere, Voltage in volts, Electric energy in \[Kwh\]

Complete step by step solution
To find the Electric current in the circuit.
               We use electric power is given by
          $\begin{align}
  & P=VI \\
 & P\text{ is power }P=4Kw \\
 & V\text{ is voltage }V=220V \\
 & I\text{ is current }I=? \\
 & I=\dfrac{P}{V}=\dfrac{4Kw}{220V} \\
\end{align}$
          $\begin{align}
  & I=\dfrac{4\times 1000}{220} \\
 & =\dfrac{200}{11} \\
 & =18\cdot 18A \\
\end{align}$
To find the Resistance of heater,
We use ohm’s law
     $\begin{align}
  & V=IR \\
 & R=\dfrac{V}{I}=\dfrac{220V}{18\cdot 18I} \\
 & R=12\cdot 1012\text{ }ohm \\
\end{align}$
To find energy consumed in 2 hour,
$\begin{align}
  & \text{Electric energy}=\text{Power}\times \text{Time} \\
 & \text{ }=4Kw\times 2hr \\
 & \text{ }=8Kwh \\
\end{align}$

Note: Keep all the units in $SI$ system or all in $CGS$ system.
We can also use, $\text{Power}={{I}^{2}}R$
Or $\begin{align}
  & \text{Power}=\dfrac{{{V}^{2}}}{R}\,\text{ }\left( \text{ To find resistance} \right) \\
 & \text{Try the above question, with this formula}\text{.} \\
\end{align}$