Question

You are given $5m$ length of heating wire, it has resistance of $24\Omega$. It is cut into two and connected to $110$ volt line individually. The total power for the two half lengths is:

• A. 500 watts
• B. 1000 watts
• C. 2000 watts
• D. 2500 watts

Answer 1

Answer: (C)

2000 watts

Resistance of the full wire $=24ohm$

Since resistance is directly proportional to length.
$\therefore$ Resistance of the half wire $=\frac{1}{2}\times 24=12ohm$
Power in one half $=V.I.$

and $V=IR$ $I=\frac{V}{R}$ $V=110volts$ $R=12ohms$
Power in one half= $=110\times \frac{110}{12}$
$=55\times \frac{55}{3}watts$
Total power of two half lengths $=2\times 55\times \frac{55}{3}=\frac{6050}{3}$
$=2000watts$ (approximately)