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electricity — Science STD 10 — Question

Gujarat BoardEnglish MediumSTD 10Scienceelectricity3 Marks
Question
If the current $l$ through a resistor is increased by $100\%$ (assume that the temperature of the resistor remains unchanged), find the percentage increase in power dissipated.
✓

Answer

  • Power dissipated $P =I^2 R$
  • Current after increased by $100 \%=l^{\prime}$
  • $=I+\frac{100 I}{100}$
  • $=2 I$
  • So, new power $P ^{\prime}=I^{\prime 2} R =(2 I)^2 R =4 I^2 R$
  • $\therefore \text { Percentage increa }$
  • $=\frac{p^{\prime}-P}{P} \times 100 \%$
  • $=\frac{4 I^2 R-l^2 R}{I^2 R} \times 100 \%$
  • $=\frac{I^2 R(4-1)}{I^2 R} \times 100 \%$
  • $=3 \times 100 \%$
  • $=300 \%$
  • $\therefore \text { Percentage increase in power dissipation }$

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