Compare the power used in the 2 ,Omega resist | vedclass

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(C) Case $(i)$: Potential difference,$V = 6 \,V$. The $1 \,\Omega$ and $2 \,\Omega$ resistors are connected in series. The equivalent resistance $R =

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Power in $(i)$ is equal to $(ii)$

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(C) Case $(i)$: Potential difference,$V = 6 \,V$. The $1 \,\Omega$ and $2 \,\Omega$ resistors are connected in series. The equivalent resistance $R = 1 + 2 = 3 \,\Omega$. According to Ohm's law,$I = V/R = 6/3 = 2 \,A$. In a series circuit,the current remains the same through all components. Thus,the current through the $2 \,\Omega$ resistor is $2 \,A$. Power $P = I^2 R = (2)^2 	imes 2 = 8 \,W$.Case $(ii)$: Potential difference,$V = 4 \,V$. The $12 \,\Omega$ and $2 \,\Omega$ resistors are connected in parallel. In a parallel circuit,the voltage across each component is the same as the source voltage. Thus,the voltage across the $2 \,\Omega$ resistor is $4 \,V$. Power $P = V^2/R = (4)^2/2 = 16/2 = 8 \,W$.Conclusion: The power used in the $2 \,\Omega$ resistor is $8 \,W$ in both cases.

$I$ (amperes)	$0.5$	$1.0$	$2.0$	$3.0$	$4.0$
$V$ (volts)	$1.6$	$3.4$	$6.7$	$10.2$	$13.2$

Compare the power used in the $2 \,\Omega$ resistor in each of the following circuits: $(i)$ a $6 \,V$ battery in series with $1 \,\Omega$ and $2 \,\Omega$ resistors,and $(ii)$ a $4 \,V$ battery in parallel with $12 \,\Omega$ and $2 \,\Omega$ resistors.

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