Question

Compare the power used in the 2 Ω resistor in each of the following circuits:

1. a 6 V battery in series with 1 Ω and 2 Ω resistors,
2. a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Answer 1

(i) Potential difference, \(V = 6\  V\)
\(1 \ Ω\) and \(2 \ Ω\) resistors are connected in series. Therefore, equivalent resistance of the circuit,
\(R = 1 + 2 = 3\ Ω\)
According to Ohm’s law,
\(V = IR\)
Where,
\(I\) is the current through the circuit
\(I=  \frac 63  = 2 A\)
This current will flow through each component of the circuit because there is no division of current in series circuits. Hence, current flowing through the \(2 \ Ω\) resistor is \(2\ A\). Power is given by the expression,
\(P= I^2R \)
\(P = 2^2 \times 2 \)
\(P = 8 \ W\)

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(ii) Potential difference, \(V = 4\ V\)
\(12 \ Ω\) and \(2\  Ω\) resistors are connected in parallel. The voltage across each component of a parallel circuit remains the same. Hence, the voltage across \(2 \ Ω\) resistor will be \(4 \ V\).
Power consumed by \(2\  Ω\) resistor is given by
\(P=\) \(\frac {V_2}{R}\)

\(P = \frac {4^2}{2}\) 
\(P = 8\  W\)
Therefore, the power used by \(2\  Ω\) resistor is \(8 \ W\).