Question

For a heater rated $2.2kW$ and $220V$, calculate

1. the current
2. the resistance of the heater
3. the energy consumed in $2hours$
4. the cost if $1kWh$ is priced at $₹5$.

Answer 1

Step 1 - Given data

Power $P=2.2kW$ or $P=2200W$

(Note: $1kW=1000W$)

Voltage $V=220V$

Time $t=2h$

Step 2 - (a) Finding the current

Consider the current is $I$.

So, current can be calculated as

$$\begin{gathered} I=\frac{P}{V} \\ I=\frac{2200W}{220V} \\ I=10A \end{gathered}$$

Step 3 - (b) Finding the resistance of the heater

From the formula of Ohm's law, the resistance $R$ can be calculated as

$$\begin{gathered} R=\frac{V}{I} \\ R=\frac{220V}{10A} \\ R=22\Omega \end{gathered}$$

Step 4 - (c) Finding the energy consumed in $2hours$

Consider the energy consumed in $2hours$ is $E$.

So, energy can be calculated as

$$\begin{gathered} E=V\times I\times t \\ E=(220V)\times (10A)\times (2h) \\ E=4400Wh \\ E=4.4kWh \end{gathered}$$

Step 5 - (d) Finding the cost of $1kWh$ is priced at $₹5$

If the cost of $1kWh$ is priced at $₹5$, then the cost rate is $r=₹5perkWh$

Consider the total cost is $R$.

So, the total cost can be calculated as

$$\begin{gathered} R=E\times r \\ R=(4.4kWh)\times (₹5/kWh) \\ R=₹22 \end{gathered}$$

Final answer - a. The current is $10A$.

b. The resistance of the heater is $22\Omega$.

c. The energy consumed in $2hours$ is $4.4kWh$.

d. The cost is $₹22$.