A battery of emf 12V and internal resistance 2 Ω is connected to a 4 resistor as shown in the figure.
(a) Show that a voltmeter when placed across the cell and across the resistor, in turn, gives the same reading.
(b) To record the voltage and the current in the circuit, why is voltmeter placed in parallel and ammeter in series in the circuit?
Answers
(a) voltage across the voltage source and the resistor is same.
(b) voltmeter is placed in parallel and ammeter in series in a circuit.
(a)
#According to ohm's law, voltage is directly proportional to the current flowing through an ohmic component.
# V = I*R
V is voltage, I is current and R is the resistance.
Total current flowing in the circuit = total voltage divided by the total resistance offered by all the components in the circuit.
I = V/ R total
R total = (4 + 2) ohms
# Since the voltage source has an internal resistance of 2ohms, it is included in the calculation of total resistance.
# Now, the total current flowing through the circuit = 12/(4+2)
= 12/6
There fore, total current= 2 Amperes
# Voltage across the 4 ohm resistor = current through the resistor multiplied by the resistance. (V = I*R)
Voltage at 4ohm = 2A * 4ohm
= 8 volts.
# voltage across the voltage source is calculated below.
V = Vs - (Rin*I)
Vs is the source voltage, Rin is the internal resistance, I is the current through the source.
V = 12 - (2*2)
V= 12 - 4
V = 8 volts.
Thus, voltage across the voltage source and the resistor is same.
(b)
# an ideal voltmeter has infinite internal resistance. And an ideal ammeter has zero internal resistance.
# for an ammeter to calculate the amount of current flowing, all the current has to flow through it. So, even if an ammeter is attached in series, the working of the circuit doesn't change; as it acts like a conducting wire or short circuit because of its very low internal resistance.
But, this is not the case when an ammeter is connected in parallel. In this situation, all the current flows through the ammeter and not the components of the circuit which changes the working of the circuit.
# A voltmeter measures the potential difference between two points in a circuit. If it is connected in series, no current would flow through the circuit because of the high resistance.
When a voltmeter is connected in parallel, it doesn't change the circuit properties as no current flows through it. And thus calculates the potential difference.
Thus, voltmeter is placed in parallel and ammeter in series in a circuit.
