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Answer :
(i) Potential difference, V = 6 V
1 R and 2 R resistors are connected in series. Therefore, equivalent resistance of the circuit,
Resistance = 1 + 2 = 3 R
According to Ohm’s law,
V = IR
Where,
I is the current through the circuit
I= \(\frac{6}{3} \) = 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 \(\Omega \) resistor is 2 A. Power is given by the expression,
P= (I)2R = (2)2 x 2 = 8 W
(ii) Potential difference, V = 4 V
12 R and 2 R resistors are connected in parallel. The voltage across each component of a parallel circuit remains the same. Hence, the voltage across 2 R resistor will be 4 V.
Power consumed by 2 \(\Omega \) resistor is given by
\( P= \frac{V_2}{R} = \frac{42}{2} = 8 W \)
Therefore, the power used by 2 R resistor is 8 W.