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,
$P= I^2R$
$P = 2^2 \times 2$
$P = 8 \ W$

---

(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 $8 \ W$.