The resistance and the magnitude of the current depend on the path that the curr

Question

The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from a material whose resistivity is ? = 1.50 x 10-2 ?*m, and the unit of length in the drawing is L0 = 5 cm. Each piece of material is connected to a 3.00-V battery. Find (a) the resistance and (b) the current in each case.

The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from a material whose resistivity is ? = 1.50 x 10-2 ?*m, and the unit of length in the drawing is L0 = 5 cm. Each piece of material is connected to a 3.00-V battery. Find (a) the resistance and (b) the current in each case.

Explanation / Answer

R = rho * L / A where rho is resistivity, L is length of wire and A is area of cross section

(a) here area of cross section = 2Lo * Lo = 2 L^2 = 2 * 5^2 = 50 cm^2 = 5 * 10^-3 m^2

and length = 4*Lo = 20 cm = 0.2 m

so R = 1.5 * 10^-2 * 0.2 / (5 * 10^-3) = 0.6 ohm

So current = V / R = 3 / 0.6 = 5 A

(b) here area of cross section = 2 Lo * 4 Lo = 8 Lo^2 = 8 * 5^2 = 200 cm^2 = 0.02 m^2

and length = Lo = 5cm = 0.05 m

so R = 1.5 * 10^-2 * 0.05 / 0.02 = 0.0375 ohm

so current = 3 / 0.0375 = 80 A

(c) cross section ara = Lo * 4 Lo = 4 * 5^2 = 100 cm^2 = 0.01 m^2

and length = 2 Lo = 10 cm = 0.1 m

so R = 1.5 * 10^-2 * 0.1 / 0.01 = 0.15 ohm

so current = 3 / 0.15 = 20 A

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.