Question

If 5 resistors each of 5Ω resistance are connected in parallel connection with a battery. If the current flowing through cross section of wire is 10 Ampere calculate the voltage of battery by using ohms law.

Answer 1

$\Large{\underbrace{\underline{\sf{Understanding\: the\: Concept}}}}$

Here in this question, concept of ohm's law is used. We are given 5 resistors each of resistance 5Ω and also current flowing through conductor is given. We are asked to find the value of potential difference or voltage. To Find the voltage, firstly we have to find the equivalent resistance in the parallel connection of resistors and then by applying ohms law, we will get the value of voltage.

So let's find equivalent resistance!!

Resistance in parallel connection can be expressed as::

$:\implies\sf \dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\dots$

By substituting values of resistance::

$:\implies\sf \dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}$

By taking LCM::

$:\implies\sf \dfrac{1}{R}=\dfrac{1+1+1+1+1}{5}$

$:\implies\sf \dfrac{1}{R}=\dfrac{5}{5}$

$:\implies\sf \dfrac{1}{R}=1$

By cross multiplication, we get::

$:\implies\boxed{\bf R=1\Omega}$

We have obtained value of equivalent resistance.

Now applying ohm's law::

$\large\underline{\boxed{ \sf V=IR}}$

By substituting given values::

$\sf :\implies V=(10\:ampere)\times(1\Omega)$

$\boxed{\sf V=10 \:volts}$

So the required voltage or potential difference is 10 volts.