Question

find current across 3 ohm resistor if there are three resistors of 3 ohm connected to a 10 Volt battery in series.

Answer 1

Given:

Three resistors each of 3Ω

A battery of 10 Volt

To Find:

Current across one of the 3 ohm resistors

Solution:

We know that,

In series combination

• Current through each resistance is same as that of main current flowing through the circuit i.e. I=I₁=I₂=I₃=.......
• Equivalent resistance is equal to the sum of individual resistances

i.e. $\bf{R=R_{1}+R_{2}+R_{3}+.....}$

For a circuit,

$\pink{\boxed{\bf{I=\dfrac{V}{R}}}}$

where

I is current flowing through circuit

V is potential across battery

R is resistance of circuit

$\rule{190}{2}$

Now,

Let the equivalent resistance of given circuit be R

So,

$\longrightarrow\rm{R=3+3+3}$

$\longrightarrow\rm{R=9\Omega}$

Now,

Let the current flowing through the circuit be I

So,

$\longrightarrow\rm{I=\dfrac{V}{R}}$

$\longrightarrow\rm{I=\dfrac{10}{9}A}$

Therefore, current flowing through across each of the 3Ω resistor is 10/9 A.

Hence, the required current is 10/9 A.

Answer 2

Given

Resistance of three resistors = 3 ohm each

Voltage of battery = 10 Volt

To Find

Current flowing across that resistor.

Solution

As the battery is in Series, we will use series combination resistor formula :

⇒ R = R₁ + R₂ + R₃ ................

Where, R = Total resistance. R₁ , R₂ & R₃ = 1st, 2nd & 3rd resistor

Here, R₁ = R₂ = R₃ = 3 ohm.

➻ R = 3 + 3 + 3

➻ R = 9 ohm.

Here, voltage of battery given = 10 V

We know formula ↓

⇒ I = V/R

Where, I = Current, V = Voltage, R = Total resistance.

➻ I = 10/9 A

➻ I = 1.11 Ampere

∴ Current flowing through battery = 1.11 A