Question

Find the reading of the ammeter in the given circuit?

A. $0.4$
B. $1$
C. $0.6$
D. $1.2$

Answer 1

Hint : An ammeter is an electrical instrument used to measure current.
The current through each resistor connected in series is the same and voltage across the resistors connected in parallel is the same.
According to Ohm's law, voltage across a resistor is given by $V = IR$ where $I$ is the current passing through the resistor and $R$ is the resistance.

Complete Step By Step Answer:
We know that an ammeter is an electrical instrument used to measure current.
We know that the equivalent resistance in a series combination of n resistors is given by ${R_{eq}} = {R_1} + {R_2} + {R_3} + ..... + {R_n}$
And the equivalent resistance in a parallel combination of n resistors is given by $\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} + ..... + \dfrac{1}{{{R_n}}}$
As clear from the figure that $10\Omega$ and $2\Omega$ resistances are in series so their equivalent resistance ${R_1} = 10 + 2 = 12\Omega$
Similarly, $25\Omega$ and $5\Omega$ resistances are in series so their equivalent resistance ${R_2} = 25 + 5 = 30\Omega$
Now, ${R_1}$ and ${R_2}$ will be in parallel and the total equivalent resistance of the circuit is given by
$\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} = \dfrac{1}{{12}} + \dfrac{1}{{30}}$
On simplifying we have
${R_{eq}} = \dfrac{{12 \times 30}}{{12 + 30}} = 8.57\Omega$
According to Ohm's law, voltage across a resistor is given by $V = IR$ where $I$ is the current passing through the resistor and $R$ is the resistance.
We know that the voltage across the resistors connected in parallel is the same.
So, the voltage across ${R_1}$ will be given by
$V = 1.4 \times 8.57 = 11.99{\text{ V}} \approx 12{\text{ V}}$
Now, as we know that the current through each resistor connected in series is the same. So, the current through $10\Omega$ and $2\Omega$ resistances will be given by
$I = \dfrac{V}{{{R_1}}} = \dfrac{{12}}{{12}} = 1{\text{ A}}$
Therefore, reading of the ammeter is $1{\text{ A}}$ .
Hence, option B is correct.

Note :
The Ohm’s law for current electricity is applicable only when the temperature and other physical condition remains constant. Always remember that the current through each resistor connected in series is the same and voltage across the resistors connected in parallel is the same.