Question

Pls answer this asap

Answer 1

Answer :

• The equivalent resistance between A and B in the given circuit is 5 Ω.

Explanation :

Given :

For diagram PQRS ,

• Resistor in the circuit , R1 = 6 Ω
• Resistor in the circuit, R2 = 3 Ω

For diagram WXYZ ,

• Resistor in the circuit , R1 = 4 Ω
• Resistor in the circuit , R2 = 12 Ω

To find :

• The equivalent resistance between A and B.

Knowledge required :

According to the diagram , the both the circuits PQRS and WXYZ have two resistors which are in parallel circuit.

But the circuits PQRS and WXYZ are in series circuit.

Hence ,

• Sum of the equivalent resistance of PQRS and the equivalent resistance of WXYZ in the series circuit will give us the equivalent resistance between A and B.

Now,

Formula for equivalent resistance in a parallel circuit :

⠀⠀⠀1/Re = 1/R1 + 1/R2 + 1/R3 + ... +1/Rn

Where :

• Re = Equivalent resistance in the parallel circuit.

• R = Resistance in the resistors.

Formula for equivalent resistance in a series circuit :

⠀⠀⠀Re = R1 + R2 + R3 + ... + Rn

Where :

• Re = Equivalent resistance in the circuit circuit.

• R = Resistance in the resistors.

Solution :

Equivalent resistance in the circuit PQRS :

By using the equation for equivalent resistance in a parallel circuit and substituting the values in it, we get :

==> 1/Re = 1/R1 + 1/R2

==> 1/Re = 1/6 + 1/3

LCM of 6 and 3 is 6.

==> 1/Re = (1 + 2)/6

==> 1/Re = 3/6

==> 1/Re = 1/2

==> Re = 2

∴ Re = 2 Ω

Hence the equivalent resistance in the parallel circuit , PQRS is 2 Ω.

Equivalent resistance in the circuit WXYZ :

By using the equation for equivalent resistance in a parallel circuit and substituting the values in it, we get :

==> 1/Re = 1/R1 + 1/R2

==> 1/Re = 1/4 + 1/12

LCM of 4 and 12 is 12.

==> 1/Re = (3 + 1)/12

==> 1/Re = 4/12

==> 1/Re = 1/3

==> Re = 3

∴ Re = 3 Ω

Hence the equivalent resistance in the parallel circuit, WXYZ is 3 Ω.

Equivalent resistance between A and B :

Here ,

• R1 = 2 Ω
• R2 = 3 Ω

By using the equation for equivalent resistance in a series circuit and substituting the values in it, we get :

==> Re = R1 + R2

==> Re = 2 + 3

==> Re = 5

∴ Re = 5 Ω

Therefore,

• The equivalent resistance between A and B in the circuit is 5 Ω.