### Chapter 3: Electricity

Q
##### Electricity

Question:

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) The circuit diagram is shown below.

Total resistance, $R = 1\ \Omega + 2\ \Omega = 3\ \Omega$

Potential difference, $V = 6\ V$

Using Ohm’s law

$V = IR$

$I = \frac{V}{R}$

$I = \frac{6}{3} = 2\ A$

$I = 2\ A$

In series, the current does not divide, so current flowing through the 2 Ω resistance is 2 A.

Power used in 2 Ω resistor will be,

$P = I^2R$

$P = (2)^2 \times 2$

$P = 4 \times 2 = 8\ W$

$P = 8\ W$

(ii) The circuit diagram is shown below.

Potential difference, $V = 4\ V$

In parallel, the voltage remains the same for each component connected. So, the voltage across 2 Ω resistance is 4 V.

Power used in 2 Ω resistor will be,

$P = \frac{V^2}{R}$

$P = \frac{(4)^2}{2}$

$P = \frac{16}{2} = 8\ W$

$P = 8\ W$

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