Question

The same current flows through every part of the circuit containing three resistances if they in .....

• A. parallel
• B. series
• C. two of them series and then parallel with third one.
• D. two of them parallel and then series with third one.

Answer 1

The correct option is B series

Components connected in series are connected along a single path, so the same current flows through all of the components. In a series circuit, every device must function for the circuit to be complete. One bulb burning out in a series circuit breaks the circuit.
Experiment to show that the same current flows through every part of the circuit containing three resistances in series connected to a battery:

Figure 1 below shows an electric circuit in which three resistors having resistances R1, R2 and R3, respectively, are joined end to end.
Objects required:
Join three resistors of different values in series. Connect them with a battery, an ammeter and a plug key, as shown in Figure 1. You may use the resistors of values like 1 , 2 , 3 etc., and a battery of 6 V for performing this activity. A voltmeter is connected later.
Experiment:
Plug the key. Note the ammeter reading.
Change the position of ammeter to anywhere in between the resistors. Note the ammeter reading each time.
Now, insert a voltmeter across the ends X and Y of the series combination of three resistors, as shown in Figure 2.
Plug the key in the circuit and note the voltmeter reading. It gives the potential difference across the series combination of resistors. Let it be V. Now measure the potential difference across the two terminals of the battery. Compare the two values.
Take out the plug key and disconnect the voltmeter. Now insert the voltmeter across the ends X and P of the first resistor, as shown in Figure 2.
Plug the key and measure the potential difference across the first resistor. Let it be V1.
Similarly, measure the potential difference across the other two resistors, separately. Let these values be V2 and V3, respectively.
Deduce a relationship between V, V1, V2 and V3.
Observation:
We will observe that the value of the current in the ammeter is the same, independent of its position in the electric circuit. It means that in a series combination of resistors the current is the same in every part of the circuit or the same current through each resistor.
Also, we will observe that the potential difference V is equal to the sum of potential differences V1, V2, and V3. That is the total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is,
V = V1 + V2 + V3 (1)
In the electric circuit shown in Figure, let I be the current through the circuit. The current through each resistor is also I. It is possible to replace the three resistors joined in series by an equivalent single resistor of resistance R, such that the potential difference V across it, and the current I through the circuit remains the same. Applying the Ohms law to the entire circuit, we have
V = IR(2)
On applying Ohms law to the three resistors separately, we further have
V1 = I R1 (3-a)
V2 = I R2 (3-b) and
V3 = I R3 (3-c)
From Eq. (1),
I R = I R1 + I R2 + I R3
Or
Rs = R1 +R2 + R3
We can conclude that when several resistors are joined in series, the resistance of the combination Rs equals the sum of their individual resistances, R1, R2, R3, and is thus greater than any individual resistance.
Hence, this experiment proves that the same current flows through every part of the circuit containing three resistances in series connected to a battery.