Question

An ammeter, voltmeter and a resistor are connected in series to a cell and the readings are noted as I and V . If another resistor R is connected in parallel with voltmeter , then:
$A.$ $I$ and $V$ increases
$B.$ $I$ increases
$C.$ $I$ and $V$ will remain same
$D.$ $I$ decreases
$E.$ $I$ remains constant

Answer 1

- Hint: When a resistor is connected in parallel then total resistance of the setup decreases. Now use knowledge of the effect of decrease in resistance on potential difference and current to get the answer.

Complete step-by-step solution -

As we know that when we add a resistor in parallel then total resistance of the system is decreased because if there is a resistor $R_1$ and if another resistor ${R_2}$ is connected in parallel the effective resistance is given by,
${R_{total}}$ =$\dfrac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}$
As we can see that total resistance is less than both ${R_1}$ and ${R_2}$
Relation of current with resistance is given as,
$I = \dfrac{V}{R}$
Now since current is inversely proportional to resistance so current will increase hence reading across ammeter will increase.
Now potential difference across voltmeter can be found by,
${V_{voltmeter}} = {V_{total}} - {V_{ammeter}}$
Now put value of ${V_{ammeter}}$ in above equation,
${V_{voltmeter}} = {V_{total}} - i({R_{ammeter}})$
Now since the current across ammeter is increasing so potential difference across voltmeter will decrease .
So option B will be the correct answer.

Additional Information:
Ohm's law states that the electrical current flowing in a circuit is proportional to the voltage and inversely proportional to the resistance . Therefore, if the voltage is increased, the current will increase if the resistance of the circuit is not changed. Similarly, increasing the resistance of the circuit will decrease the current flow if the voltage is not changed.

Note: When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, therefore the total resistance is lower. Each resistor in parallel has an equivalent full voltage of the source applied thereto , but divide total current amongst them.