Question

A bulb is rated at $200V–100W$. What is its resistance? Five such bulbs burn for $4hours$. What is the electrical energy consumed? Calculate the cost if the rate is $50paiseperunit$.

Answer 1

Step 1. Given data

Voltage is, $V=200V$

The power is, $P=100W$

The running time for five bulbs is, $t=4h$

Per unit cost is $=50paise=0.50rupee$.

Step 3. Finding resistance

Resistance of the bulb, $R=\frac{V^2}{P}$. Where, $V$ is the voltage, $P$ is the power.

Substituting all the values,

$R=\frac{200V\times 200V}{100W}$

By solving this we get,

$R=400\Omega$.

Step 3. Finding the total energy consumed by the bulbs

$\mathrm{Total}\mathrm{energy}\mathrm{consumed}=\mathrm{Number}\mathrm{of}\mathrm{bulbs}\times \mathrm{Running}\mathrm{time}\times \mathrm{power}$

Total energy consumed$=5\times 4h\times 100W$

By solving this we get,

Total energy consumed$=2000Wh=2kWh=2units$

Step 4. Finding the total running cost of the bulbs

$\mathrm{Total}\mathrm{running}\mathrm{cost}=\mathrm{Total}\mathrm{energy}\mathrm{consumed}\times \mathrm{per}\mathrm{unit}\mathrm{cost}$

Total running cost$=2kWh\times 0.50rupee$

By solving this we get,

Total running cost$=1rupee$.

Therefore,

1. Resistance of the bulb is $\mathbf{400}\mathbf{}\mathit{\Omega }$.
2. Total energy consumed is $\mathbf{2}\mathbf{}\mathit{k}\mathit{W}\mathit{h}$.
3. Total running cost is $\mathbf{1}\mathbf{}\mathit{r}\mathit{u}\mathit{p}\mathit{e}\mathit{e}$.