Question

three resistors of 5 ohm 10 ohm and 30 ohm are connected in parallel their p.d is 20v draw circuit diagram and calculate the current through each resistor , total current and total resistance​

Answer 1

Given:

Three resistors of 5Ω, 10Ω and 30Ω are connected in parallel and potential difference 'V' across them is 20 V

To Find:

• The current through each resistor

• Total current

• Total resistance​

Solution:

We know that,

• According to Ohm's law, for a conductor under certain conditions

$\pink{\boxed{\bf{V=IR}}}$

or

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

• In a parallel combination of resistors-

✏ Equivalent resistance R is given by

$\purple{\boxed{\bf{\dfrac{1}{R}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}+.....\dfrac{1}{R_{n}}}}}$

✏ Potential difference across each resistance is same

✏ Current in each resistance is different and total current I is given by

$\blue{\boxed{\bf{I=I_{1}+I_{2}+....I_{n}}}}$

$\rule{190}{1}$

Let the current through resistor of 5Ω, 10Ω and 30Ω be I₁, I₂ and I₃ respectively.

So, by applying Ohm's law on given resistors, we get

$\longrightarrow\rm{I_{1}=\dfrac{20}{5}=4A}$

$\longrightarrow\rm{I_{2}=\dfrac{20}{10}=2A}$

$\longrightarrow\rm{I_{3}=\dfrac{20}{30}=0.66A}$

$\rule{190}{1}$

Let the total current through combination be I

So,

$\longrightarrow\rm{I=I_{1}+I_{2}+I_{3}}$

$\longrightarrow\rm{I=4+2+0.66}$

$\longrightarrow\rm{I=6.66A}$

$\rule{190}{1}$

Let the total or equivalent resistance of given combination be R

So,

$\longrightarrow\rm{\dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{30}}$

$\longrightarrow\rm{\dfrac{1}{R}=\dfrac{6+3+1}{30}}$

$\longrightarrow\rm{\dfrac{1}{R}=\dfrac{\cancel{10}}{\cancel{30}}}$

$\longrightarrow\rm{\dfrac{1}{R}=\dfrac{1}{3}}$

$\longrightarrow\rm{R=3\:\Omega}$

Answer 2

Answer:R1=5 ohm, R2 =10 ohm, R3=30 ohm V=20v

Let current flowing through R1,R2,R3 be I1, I2, I3

SO, I1=V/R1

20/5=4A

I2= V/R2

= 20/10=2A

I3= V/R3

I3= 20/30

=2/3

=0.67A

Total resistance =1/R=1/R1+1/R2+1/R3

=1/5+1/10+1/30

=3 Ohm

Total current = V/R

=20/3

=6.66A

To

Explanation: