Question

(b) Two metallic rods, each of length L, area of cross section A1 and A2, having resistivity p1 and p2 are connected in parallel across a d,c battery. Obtain the expression for the effective resistivity of this ccombinationTwo

Answer 1

Answer:

Given –

• Length of both rods = L m.
• Area of cross section of rod 1 = A1.
• Area of cross section of rod 2 = A2.
• Resistivity of rod 1 = p1.
• Resistivity of rod 2 = p2.
• Connection is parallel.

To Find –

• Expression for the effective resistance of this combination.

Solution –

We know that : R = rho*l/A.

The Resistance of rod 1 will be R1 and the Resistance of rid 2 will be R2.

Hence, total resistance = 1/R1 + 1/R2.

Now, Substituting the values :

➸ 1/R1 + 1/R2 = 1/(p1 + p2) * (A1 + A2)/L

➸ 1/R1 + 1/R2 = (A1 + A2)/L(p1 + p2)

➸ (R2+R1)/R1R2 = (A1+A2)/L(p1+p2)

➸ R1R2/(R1+R2) = p1+p2 L/(A1+A2)

➸ R_eq = R1R2/(R1+R2) = p1+p2 L/(A1+A2)

FACTORS ON WHICH RESISTANCE DEPEND –

• Resistance is directly proportional to the length of the wire.
• Resistance is indirectly proportional to area of cross section of the wire.
• Resistance is depends on the nature of material of the wire.

Hence, R ∝ l and R ∝ 1/A.

➸ R ∝ l/A

➸ R = rho*l/A