Question

calculate equivalent resistance between A and B , and between a and b.
please answer...it's urgent​

Answer 1

( i )

Observe attachment for entire scenario .

This question will be solved by potential method .

It is defined as when there is no resistance b/w two points in a circuit , voltage passing through them will be zero . [ ∵ V = IR ]

As there is no resistance b/w the points P and Q  , R and S ,so voltage across b/w the point will be zero . So circuit will become ( See 2nd figure from the attachment )

2 Ω  , 4 Ω are connected in series ,

➠ 2 Ω + 4 Ω

➠ 6 Ω

8 Ω , 6 Ω are connected in series again ,

➠ 8 Ω + 6 Ω

➠ 14 Ω

Now these 4 Ω , ( 2Ω , 4Ω ) , ( 8Ω , 6Ω ) , 4 Ω are connected in parallel ,

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{14}+\dfrac{1}{4}$

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{14}$

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{2}{3}+\dfrac{1}{14}$

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{31}{42}$

$:\implies \sf R_{eq}=\dfrac{42}{31}$

$:\implies \textsf{\textbf{R _{\text{eq}}=\text{1.35} }}\ \bf{\Omega}\ \; \pink{\bigstar}$

So , Eq. resistance b/w A and B is 1.35 Ω

( ii )

Observe 2nd attachment for 2nd circuit scenario .

Observe 2nd figure in 2nd attachment ,

30Ω , 20Ω are connected in parallel ,

➠  $\sf \dfrac{1}{R_{p}}=\dfrac{1}{30}+\dfrac{1}{20}$

➠ $\sf \dfrac{1}{R_p}=\dfrac{5}{60}$

➠ Rₚ = 12 Ω

( 30Ω , 20Ω ) , 4Ω are connected in series ,

➠ 12 Ω + 4 Ω

➠ 16 Ω

Now 40Ω , 60Ω , ( (30Ω , 20Ω) , 4Ω ) are connected in parallel .

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{1}{40}+\dfrac{1}{60}+\dfrac{1}{16}$

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{3+2}{120}+\dfrac{1}{16}$

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{1}{24}+\dfrac{1}{16}$

$:\implies \sf \dfrac{1}{R_{eq}}=\dfrac{2+3}{48}$

$:\implies \sf R_{eq}=\dfrac{48}{5}$

$:\implies \textsf{\textbf{R _{\text{eq}}=\text{9.6\ } }}\bf{\Omega}\ \; \green{\bigstar}$

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn :- \: \star}}}}}$

Calculate equivalent resistance between A and B , and between a and b.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

Equivalent resistance between A and B is 1.35 Ω.

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

Voltage ↠ zero

• There is no resistance b/w two points in a circuit , voltage passing through them will be zero .

• There is no resistance b/w the points P and Q also, hence voltage across b/w the point will be zero here too .

$\Large{\underline{\underline{\bf{Find:-}}}}$

❥ Equivalent resistance between A and B .

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Let's find out current first .

So circuit will become

As we know in Figure 1 the circuits are connected in series so ,

RT = R1 + R2 + R3.

2 Ω  , 4 Ω ( In Figure 1 ) ,

↠2 Ω + 4 Ω

↠ 6 Ω

Same formula for this too

8 Ω , 6 Ω are connected in series too

↠8 Ω + 6 Ω

↠ 14 Ω

Therefore ,

As we see 4 Ω , ( 2Ω , 4Ω ) , ( 8Ω , 6Ω ) , 4 Ω are connected in parallel

Formula required :-

1/Rt = 1/R1 + 1/R2 + 1/R3

$\sf \dfrac{1}{R_{eq}}=\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{14}+\dfrac{1}{4}$

$\sf \dfrac{1}{R_{eq}}=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{14}$

$\sf \dfrac{1}{R_{eq}}=\dfrac{2}{3}+\dfrac{1}{14}$

$\sf \dfrac{1}{R_{eq}}=\dfrac{31}{42}$

$\sf R_{eq}=\dfrac{42}{31}$

Answer:-

$\yellow{\bigstar}$ $\large{\rm\purple{E .R = 1 . 35 ohms }}$

$\mathfrak{\huge{\pink{\underline{\underline{Hence}}}}}$

Equivalent resistance b/w A and B is 1.35 Ω

Additional Information :-

✮ What is Resistance ?

Resistance refer to the property of materials that allow the flow of electric current. Resistance certainly opposes the flow of current. Furthermore, the unit of resistance is ohms which is represented by the Greek uppercase letter omega Ω.

✮ Formula for Resistance ?

Resistance = voltage drop across a resistor/ current flowing through a resistor

R = \(\frac{V}{I}\)

R = resistance (Ohms, Ω)

V = voltage difference which is between the two ends of a resistor (Volts, V)

I = the current which flows through a resistor (Amperes, A)

✮ Formula to find resistance in a series circuit ?

Series circuits

The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: equivalent resistance of resistors in series :

R = R1 + R2 + R3 + ...

A series circuit is shown in the diagram above. The current flows through each resistor in turn.

✮ Formula to find resistance in a parallel circuit ?

You can find total resistance in a Parallel circuit with the following formula:

1/Rt = 1/R1 + 1/R2 + 1/R3 +..

Note :-

If one of the parallel paths is broken, current will continue to flow in all the other paths.

The total resistance of a parallel circuit is NOT equal to the sum of the resistors (like in a series circuit).