Name: Ohm’s Law & Introduction to Electric Resistance
Uploaded: 2019-07-19
Duration: 8 min 43 s
Description: In our attempt to establish a relationship between current and voltage, we will discover a new physical quantity in this video. Let's watch and learn.

Question

Two identical immersion heaters are to be used to heat water in a large container. Which one of the following arrangement would heat the water faster;

(i) connecting the heaters in series with the main supply,

(ii) connecting the heaters in parallel with the main supply?

Accepted Answer

Let the resistance of the two identical immersion heaters be $R_{1}$ and $R_{2}$ where $R_{1} = R_{2} = R$ .
The time for which the immersion heaters are used be $t$ .
The potential difference supplied by the main be $V$ .
When the immersion heaters are connected in series with the main supply their equivalent resistance is given by $R_{s} = R_{1} + R_{2} = R + R = 2 R$ .
And the heat generated is given by:
$H_{s} = \frac{V^{2}}{R_{s}} \times t = \frac{V^{2}}{2 R} \times t$

When the immersion heaters are connected in parallel with the main supply their equivalent resistance is given by $\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}$
$\Rightarrow R_{p} = \frac{R}{2}$
And the heat generated is given by:
$H_{p} = \frac{V^{2}}{R_{p}} \times t = \frac{V^{2}}{\frac{R}{2}} \times t = 2 \frac{V^{2}}{R} \times t$
Now, taking the ratio of the heat generated while the immersion heaters are connected in parallel to the heat generated while the immersion heaters are connected in series is given by:
$\frac{H_{p}}{H_{s}} = \frac{2 \frac{V^{2}}{R} \times t}{\frac{V^{2}}{2 R} \times t} = 4$
$\Rightarrow H_{p} = 4 H_{s}$
Thus, the heat generated when the immersion heaters are connected in parallel is four times more than that while they are connected in series. So, water will be heated faster when the immersion heaters are connected in parallel.

Two identical immersion heaters are to be used to heat water in a large container. Which one of the following arrangement would heat the water faster;

(i) connecting the heaters in series with the main supply,

(ii) connecting the heaters in parallel with the main supply?

Important Questions on Electricity

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