When two resistances R1 and R2 are connected in series, they consume 12 W power. When they are connected in parallel, they consume 50 W power. What the ratio of the powers of R1 and R2 ?

Question

When two resistances R1 and R2 are connected in series, they consume 12 W power. When they are connected in parallel, they consume 50 W power. What the ratio of the powers of R1 and R2 ? (A) 1/4 (B) 4 (C) 3/2 (D) 3

Tardigrade Admin · Accepted Answer

In series, ps=(P1× P2/P1+P2)=12W In parallel, Pp=P1+P2=50 W ∴ P1P2=12× 50=600 Now, (p1-p2)2=(p1+p2)2-4p1p2 =(50)2-4× 600 =2500-2400=100 ∴ P1-P2=10 or P1=30W,P2=20 W ∴ (P1/P2)=(3/2)

Q. When two resistances R1​ and R2​ are connected in series, they consume 12W power. When they are connected in parallel, they consume 50W power. What the ratio of the powers of R1​ and R2​ ?

1/4

4

3/2

3

1

In series, ps​=P1​+P2​P1​×P2​​=12W In parallel, Pp​=P1​+P2​=50W ∴ P1​P2​=12×50=600 Now, (p1​−p2​)2=(p1​+p2​)2−4p1​p2​ =(50)2−4×600 =2500−2400=100 ∴ P1​−P2​=10 or P1​=30W,P2​=20W ∴ P2​P1​​=23​

Q. When two resistances $R_{1}$ and $R_{2}$ are connected in series, they consume $12 W$ power. When they are connected in parallel, they consume $50 W$ power. What the ratio of the powers of $R_{1}$ and $R_{2}$ ?