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(a) How will you infer with the help of an experiment that the same current flows through every part of a circuit containing three resistors in series connected to a battery?
(b) Consider the given circuit and find the current flowing in the circuit and potential difference across the 15 Ω resistor when the circuit is closed.
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(a) With the help of an experiment given below, we can infer that the same current flows through every part of a circuit containing three resistors in series connected to a battery.

Let's take three resistors $R_1, R_2\ and\ R_3$ of different values, connected in series. Connect them with a battery, an ammeter, and a plug key. When the plug key is closed then the ammeter reading is recorded. Now, the position of the ammeter is changed to anywhere in between the resistors again, the ammeter reading is recorded each time. According to the ammeter readings, it's observed that there was identical reading each time, which shows that the same current flows through every part of the circuit containing three resistances in series connected to a battery.


(b) Given:

Resistance of the resistor, $R_1=5\Omega$

 Resistance of the resistor, $R_2=10\Omega$

 Resistance of the resistor, $R_3=15\Omega$

Potential difference, $V=30V$

To find: Current flowing in the circuit, $I$.

Solution:

In the given figure, all the resistors are connected in series. 

We know that in series combination total resistance is given as-

$R_S=R_1+R_2+R_3$

Substituting the given values we get-

$R_S=5+10+15$

$R_S=30\Omega$

Thus, the total resistance of the circuit is 30 Ohm.


From Ohm's law, we know that-

$I=\frac {V}{R}$

Putting the value of $V$ and $R$, we get-

$I=\frac {30}{30}$

$I=1A$

Thus, the current flowing in the circuit is 1 Ampere.


Now, to find the potential difference across $15\Omega$ resister we use Ohm's law-

$V=I\times R$

Putting the value of $I=1A$ and $R=15\Omega$, we get-

$V=1\times 15$

$V=15V$

Thus, the potential difference across $15\Omega$ resister is 15 Volt.

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Updated on: 10-Oct-2022

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