JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors Question Bank Heating Effect of Current

  • question_answer Two bulbs of 500 watt and 200 watt are manufactured to operate on 220 volt line. The ratio of heat produced in 500 W and 200 W, in two cases, when firstly they are joined in parallel and secondly in series, will be [MP PET 1996; DPMT 1999]

    A)            \[\frac{5}{2},\,\frac{2}{5}\]    

    B)            \[\frac{5}{2},\,\frac{5}{2}\]

    C)            \[\frac{2}{5},\,\frac{5}{2}\]    

    D)            \[\frac{2}{5},\,\frac{2}{5}\]

    Correct Answer: A

    Solution :

               Resistance \[{{R}_{1}}\] of  500 W bulb \[=\frac{{{(220)}^{2}}}{500}\] Resistance \[{{R}_{2}}\] of  200 W bulb \[=\frac{{{(220)}^{2}}}{200}\] When joined in parallel, the potential difference across both the bulbs will be same. Ratio of heat produced \[=\frac{{{V}^{2}}/{{R}_{1}}}{{{V}^{2}}/{{R}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{5}{2}\] When joined in series, the same current will flow through both the bulbs. Ratio of heat produced \[=\frac{{{i}^{2}}{{R}_{1}}}{{{i}^{2}}{{R}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{2}{5}\]

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