Question

Three resistances of 20,10 and 5 ohms are connected in parallel across 6V battery. Calculate current through 10 ohm resistance

Answer 1

Question :-

Three resistances of 20,10 and 5 ohms are connected in parallel across 6V battery. Calculate the total current & current flowing through 10 ohm resistance

Given :-

Three resistors of 20Ω , 10Ω & 5Ω are connected in parallel across a 6V battery

Required to find :-

• Calculate the current passing through 10Ω resistor ?

Law used :-

Ohm's law ;

V = IR

Here,

V = Voltage or Electromotive force ( EMF )

I = Current

R = Resistance

Solution :-

Given Information :-

Three resistors of 20Ω , 10Ω & 5Ω are connected in parallel across a 6V battery

we need to find the current passing through the 10 ohm resistor .

So,

In order to find the current flowing through the 10 ohm resistor .

Firstly ,

we should find the total current flowing in this circuit .

This implies ;

Using the ohm's law we can find the current because the values of Voltage is given .

And,

we need to find the Equivalent Resistance in this 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 ;

$\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1 }{ 20 \Omega } + \dfrac{ 1}{ 10 \Omega } + \dfrac{ 1}{ 5 \Omega } }$

$\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1 + 2 + 4 }{ 20 \Omega } }$

$\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 7}{ 20 } \Omega }$

$\tt{ {R}_{eq} = \dfrac{20}{ 7 } \Omega }$

Hence,

• Equivalent Resistance = 20/7 Ω

Using the ohm's law ;

➥ V = IR

➥ 6 = I x 20/7

➥ I x 20/7 = 6

➥ I = 6 x 7/20

➥ I = 42/20

➥ I = 21/10

➥ I = 2.1 A

Hence,

• Total current = 2.1 A

Now let's find the current flowing through the 10Ω resistor ;

Since,

we know that in a parallel combination the potential difference is constant .

So,

Using the Ohm's law ;

➥ V = IR

➥ 6 = I x 10

➥ 6 = 10I

➥ 10I = 6

➥ I = 6/10

➥ I = 0.6 A

Hence,

• Current flowing through 10 ohm resistor = 0.6 A

Answer 2

Answer:

Question :-

Three resistances of 20,10 and 5 ohms are connected in parallel across 6V battery. Calculate the total current & current flowing through 10 ohm resistance

Given :-

Three resistors of 20Ω , 10Ω & 5Ω are connected in parallel across a 6V battery

Required to find :-

Calculate the current passing through 10Ω resistor ?

Law used :-

Ohm's law ;

V = IR

Here,

V = Voltage or Electromotive force ( EMF )

I = Current

R = Resistance

Solution :-

Given Information :-

Three resistors of 20Ω , 10Ω & 5Ω are connected in parallel across a 6V battery

we need to find the current passing through the 10 ohm resistor .

So,

In order to find the current flowing through the 10 ohm resistor .

Firstly ,

we should find the total current flowing in this circuit .

This implies ;

Using the ohm's law we can find the current because the values of Voltage is given .

And,

we need to find the Equivalent Resistance in this 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 }}}

R

eq

1

=

R

1

1

+

R

2

1

+

R

3

1

……

This implies ;

\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1 }{ 20 \text{\O}mega } + \dfrac{ 1}{ 10 \text{\O}mega } + \dfrac{ 1}{ 5 \text{\O}mega } }

R

eq

1

=

20Ømega

1

+

10Ømega

1

+

5Ømega

1

\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1 + 2 + 4 }{ 20 \text{\O}mega } }

R

eq

1

=

20Ømega

1+2+4

\tt{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 7}{ 20 } \text{\O}mega }

R

eq

1

=

20

7

Ømega

\tt{ {R}_{eq} = \dfrac{20}{ 7 } \text{\O}mega }R

eq

=

7

20

Ømega

Hence,

Equivalent Resistance = 20/7 Ω

Using the ohm's law ;

➥ V = IR

➥ 6 = I x 20/7

➥ I x 20/7 = 6

➥ I = 6 x 7/20

➥ I = 42/20

➥ I = 21/10

➥ I = 2.1 A

Hence,

Total current = 2.1 A

Now let's find the current flowing through the 10Ω resistor ;

Since,

we know that in a parallel combination the potential difference is constant .

So,

Using the Ohm's law ;

➥ V = IR

➥ 6 = I x 10

➥ 6 = 10I

➥ 10I = 6

➥ I = 6/10

➥ I = 0.6 A

Hence,

Current flowing through 10 ohm resistor = 0.6 A