Question

A heater coil is rated $100 \,W$, $200 \,V$. It is cut into two idential parts. Both parts are connected together in parallel, to the same source of $200 \,V$. The energy liberated per second in the new combination is

• A. $100\,J$
• B. $200\,J$
• C. $300\,J$
• D. $400\,J$

Answer 1

Answer: (D)

Resistance of heater coil,
$R=\frac{V^{2}}{P}=\frac{200 \times 200}{100}$
$=400\,\Omega$.
Resistance of either half part $= 200\,\Omega$.
Equivalent resistance when both parts are connected in parallel.
$R'=\frac{200 \times200}{200+200}$
$=100\,\Omega$.
Energy liberated per second when combination is connected to a source of $200 \,V$,
$=\frac{V^{2}}{R'}=\frac{200 \times 200}{100}$
$=400\,J$.