Question

Teo resistors R1 and R2 are connected in series has a total resistance 6 ohm. Ehen they are connected in parallel,the e1uivalent resistance in combination is 1.5 ohm.Calculate the value of R1 and R2.

Answer 1

Answer:

3 ohms, 3 ohms

Explanation:

Given :

• R1 and R2 when connected in series give an equivalent resistance of 6 ohms

• R1 and R2 when connected in parallel give an equivalent resistance of 1.5 ohms

To find :

• Value of R1 and R2

When two resistors are connected in series :

Equivalent resistance = R1+R2

6=R1+R2 - - - (1)

When two resistors are connected in parallel:

equivalent resistance = R1×R2/R1+R2

1.5 = R1 ×R2/R1+R2

R1+R2=6 ohms

1.5=R1×R2/6

9=R1×R2 - - - - (2)

By solving equation 1 and 2

R1= 3 Ohms

R2= 3 Ohms

Answer 2

Given:-

• Two resistors R1 and R2 are connected in series has total resistance =6 ohm.

• R1 and R2 connected in parallel which have equivalent resistance in combination =1.5 Ohm.

To Find:-

• Value of R1 and R2

Solution :-

✰ According to the question ✰

➭ When two or more resistors are joined in series, the resistance of the combination Rs is equal to the sum of their individual Resistance

Rs = R1+R2 ( Rs means resistance in series)

6 = R1 +R2....................................(i)

➭ When two or more resistors are joined in parallel, the resistance of the combination Rp is equal to the sum of the reciprocals of the individual resistances.

Rp = 1/R1 + 1/R2

1.5 = 1/R1 + 1/R2

1.5 = R1× R2/6 ..... (by using equation i R1+R2 = 6)

1.5×6 = R1 × R2

9 = R1 × R2 .......................(ii)

From equation (i) and (ii) we get

R1 = 3 Ω

And,

R2 = 3 Ω

The value of R1 is 3 Ωand R2 is 3 Ω.