Question

Raman's air-conditioner consumes 2160 W of power when a current of 9.0 A passes through it.
i) What is the voltage drop when the air-conditioner is running?
ii) How does this compare to the usual household voltage?
iii) What would happen if Raman tried connecting his air-conditioner to a 120 V line?

Answer 1

Given:

Raman's air-conditioner consumes $2160W$ of power when a current of $9.0A$ passes through it.

(i) We know,

$P=VI$

$P$; power

$V$; applied voltage

$I$; current

$\Rightarrow V=\frac{P}{I}$

$\Rightarrow V=\frac{2160}{9}$

$\Rightarrow V=240V$

Hence the voltage drop when the AC is running is $240V$

(ii) It is a little higher than domestic power supply voltage i.e., $220V$

(iii) Since the resistance of the air conditioner is constant when it is connected to a supply line of $120V$, the current decreases by half. i.e., $I=4.5A$, as voltage is getting reduced by half $\frac{240}{2}=120V$. And according to Ohm's law, $V=IR$ i.e., voltage is directly is proportional to current. Hence AC will not operate.