Question

An ideal ammeter (zero resistance) and an ideal voltmeter (infinite resistance) are connected as shown in fig. The ammeter and the voltmeter readings are:

A.)$6.25A,3.75V$
B.)$0.00A,20V$
C.)$3.00A,5V$
D.)$6.00A,6.25V$

Answer 1

Hint: An ideal voltmeter will have infinite resistance, and so is connected in parallel in a circuit. An ideal ammeter will have zero resistance and so is connected in series in a circuit.

Complete step by step answer:
The equivalent resistance is where the aggregate resistance connected either in parallel or series is calculated. Resistor circuits that combine series and parallel resistors networks together are generally known as Resistor Combination or mixed resistor circuits. The method of calculating the circuit’s equivalent resistance is the same as that for any individual series or parallel circuit.

From the given figure the equivalent resistance R of the combination is

$R=\dfrac{{{R}_{1}}\times {{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}+{{R}_{3}}$
$R=\dfrac{5\times 15}{5+15}+1.25$
$R=\dfrac{75}{20}+1.25$
\[\therefore R=5\Omega \]

Hence the current I through the circuit is

$I=\dfrac{V}{R}$
$I=\dfrac{20}{5}A=4A$

Now, current through $5\Omega $ resistance is

$I=\dfrac{V}{{{R}_{1}}}$
$\dfrac{15}{20}\times 4=3A$

Also, reading of voltmeter ${{V}_{r}}$ is equal to the potential drop across \[1.25\Omega \] resistance

${{V}_{r}}=I\times {{R}_{{{3}_{{}}}}}$
${{V}_{r}}=4\times 1.25$
${{V}_{r}}=5V$

Hence,

Reading of ammeter is $3A$
Reading of voltmeter is ${{V}_{r}}=5V$\[\]

Additional information:
The Voltmeter is a device used to measure the potential difference between two points. If we connect voltmeter in series, nothing magnificent would happen. The Voltmeter is a device of significantly high resistance, and it would impede the flow of current. Open circuit, and nothing spectacular achieved.

The Ammeter is a device of a marginally lower resistance value, since it is designed to measure the value of current in a circuit. So, it allows the current to pass through it, so as to obtain a reading. Now, if we connect an Ammeter in the parallel configuration, a large value of current would flow in the branch with the Ammeter, as current always chooses the path of least resistance. With a large amount of current flowing through the branch having the ammeter, even though alternate routes are available, the circuit would be short-circuited, and our Ammeter's wire would burn out. Essentially, it'll be damaged, and would display inaccurate readings

Therefore, Voltmeter is always connected in parallel and Ammeter is always connected in series in a circuit.

Note: During calculating the equivalent resistance, take the values of resistances in series and parallel combination appropriately.