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Compare the power used in the \(2\ Ω\) resistor in each of the following circuits:
(i) a \(6\ V\) battery in series with \(1\ Ω\) and \(2\ Ω\) resistors, and
(ii) a \(4\ V\) battery in parallel with \(12\ Ω\) and \(2\ Ω\) resistors.
(i) a \(6\ V\) battery in series with \(1\ Ω\) and \(2\ Ω\) resistors, and
(ii) a \(4\ V\) battery in parallel with \(12\ Ω\) and \(2\ Ω\) resistors.
(i) Potential difference \(=\) \(6\ V\)
The two resistors \(1\ Ω\) and \(2\ Ω\) are connected in series. Hence, the equivalent resistance is .
According to Ohm’s law, the current can be calculated using the formula
On substituting the known values, we get .
The formula to calculate power is given as
On substituting the known values, the power consumed by \(2\ Ω\) resistor is .
(ii) Potential difference \(=\) \(4\ V\)
The power consumed by \(2\ Ω\) resistor is
On substituting the known values, the power consumed by \(2\ Ω\) resistor is . From both the circuits, it can be seen that \(2\ Ω\) resistors uses .
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