Question

What is the equivalent resistance between points A and B?​

Answer 1

Hint: We have been provided with a circuit in question. Three pairs of resistance in parallel to each other and two resistances from each of the pair are in series. So apply a formula of resistance in parallel for those three pairs of resistance and then use resistance in series at point AB.

Complete answer:

The above circuit can be drawn as follows to make it easy to solve.

As you can see in given equivalent circuit diagram it shows the series combination of the resistance in the circuit which is 15Ω, 10Ω, 40Ω, 10Ω, 20Ω, 30Ω.. Let R1 be the equivalent resistance of the series combination of resistance 15Ω, 10Ω. Similarly R2 be the equivalent resistance of series. Consider Combination of resistances 40Ω, 10Ω. Consider Similarly R3 for 20Ω, 30Ω

Then R1,R2,R3 Is given as,

R1=10+15=25ΩR2=40+10=50ΩR3=20+30=50Ω

So, the circuit will look like:

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The equivalent resistance between point A and B is:

A. 32.5ΩB. 22.5Ω.C. 2.5ΩD. 42.5Ω

Answer

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Hint: We have been provided with a circuit in question. Three pairs of resistance in parallel to each other and two resistances from each of the pair are in series. So apply a formula of resistance in parallel for those three pairs of resistance and then use resistance in series at point AB.

Complete answer:

The above circuit can be drawn as follows to make it easy to solve.

As you can see in given equivalent circuit diagram it shows the series combination of the resistance in the circuit which is 15Ω, 10Ω, 40Ω, 10Ω, 20Ω, 30Ω.. Let R1 be the equivalent resistance of the series combination of resistance 15Ω, 10Ω. Similarly R2 be the equivalent resistance of series. Consider Combination of resistances 40Ω, 10Ω. Consider Similarly R3 for 20Ω, 30Ω

Then R1,R2,R3 Is given as,

R1=10+15=25ΩR2=40+10=50ΩR3=20+30=50Ω

So, the circuit will look like:

Now, these three resistances R1,R2,R3 are parallel to each other i.e. they are connected in parallel. Therefore, equivalent resistance of parallel combination is given as,

1Rp=1R1+1R2+1R3

Where, RP = equivalent resistance of parallel combination

∴1Rp=125+150+150=125+1002500=125+125⇒1Rp=225∴RP=252Ω

Now the circuit (simplified circuit) will look like:

So, the equivalent resistance RPis inn series with both resistances 2Ω and 8Ω

∴Req=Rp+2Ω+8Ω

Where, RP = equivalent resistance (final) of series combination

∴Req=2+252+8=10+252=452=22.5Ω

Hence equivalent resistance between points A and B is 22.5Ω.

Additional information:

Resistance in series: when a several number of resistances are connected in series then the equivalent resistance is equal to sum of individual resistances. If R1,R2,R3 be the resistor connected in series than their equivalent resistance R3 is given by,