Question

A 24 V potential difference is applied is applied across a parallel combination of four 6 ohm resistor. The current in each resistor is ?

a) 1 A

b) 2 A

c) 4 A

d) 16 A


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Answer 1

Answer:

net resistance =resistance÷total number of resistor.

R=6÷4=3÷2

V=IR

I=V/R

=24÷[3/2]

=[24×2]÷3

=48/3

=16 A

Answer 2

Given :-

A 24V potential difference is applied across a parallel combination of four 6 Ω resistor .

Required to find :-

• Current in each resistor ?

Law used :-

Ohm's law ;

V = IR

Here,

V = Potential difference or Electromotive force ( EMF )

I = Current

R = Resistance

Solution :-

Given data :-

A 24V potential difference is applied across a parallel combination of four 6 Ω resistor .

we need to find the current flowing in each resistor .

In order , to find the current flowing in each resistor .

Firstly,

we should find the total current flowing in the circuit .

So,

Using the ohm's law we can find the total current .

Before using it we need to find the equivalent Resistance .

Equivalent Resistance is the total resistance in the circuit

Since, the resistors are connected in parallel . The formula which we should use is ;

$\boxed{\pink{\tt{ \dfrac{ 1}{ {R}_{eq} } = \dfrac{1}{ {R}_{1} } + \dfrac{1}{ R_2 } + \dfrac{ 1}{ R_3 } \dots \dots }}}$

This implies ;

$\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1 }{ 6 \Omega } + \dfrac{ 1}{ 6 \Omega } + \dfrac{ 1}{ 6 \Omega } + \dfrac{1}{6 \Omega}}$

$\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1 + 1 + 1 + 1 }{ 6 \Omega } }$

$\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 4}{ 6 } \Omega }$

$\tt{ {R}_{eq} = \dfrac{6}{ 4 } \Omega }$

$\tt{ {R}_{eq} = \dfrac{3}{ 2 } \Omega }$

$\tt{ {R}_{eq} = 1.5 \Omega }$

Hence,

• Equivalent Resistance ( R ) = 1.5 Ω

Using the ohm's law ;

V = IR

24 = I x 1.5

I x 1.5 = 24

I = 24/1.5

I = 240/15

I = 16 A

Hence,

• Total current flowing through the circuit = 16 A

Now,

Let's find the current flowing through each resistor ;

Since, it is given that the the resistance of all 4 resistors are equal .

So,

This states the true fact that ;

The current flowing in this circuit is divided into 4 equal parts .

This implies ;

Current flowing through each resistor = Total current/No. of resistors

Current flowing through each resistor = 16A/4

Current flowing through each resistor = 4A

Therefore,

Current flowing through each resistor = 4 A