A wire made of material A has twice the length and half the cross-sectional area of a wire made of material B. If the resistivity of A is ρ, what is the resistance of wire A in terms of the resistance of wire B?
Practice Questions
1 question
Q1
A wire made of material A has twice the length and half the cross-sectional area of a wire made of material B. If the resistivity of A is ρ, what is the resistance of wire A in terms of the resistance of wire B?
2R
4R
R/2
R/4
Resistance R = ρ(L/A). For wire A, R_A = ρ(2L/(A/2)) = 4ρ(L/A) = 4R_B.
Questions & Step-by-step Solutions
1 item
Q
Q: A wire made of material A has twice the length and half the cross-sectional area of a wire made of material B. If the resistivity of A is ρ, what is the resistance of wire A in terms of the resistance of wire B?
Solution: Resistance R = ρ(L/A). For wire A, R_A = ρ(2L/(A/2)) = 4ρ(L/A) = 4R_B.
Steps: 6
Step 1: Understand the formula for resistance, which is R = ρ(L/A), where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.
Step 2: Identify the properties of wire A: it has twice the length of wire B, so L_A = 2L_B, and it has half the cross-sectional area of wire B, so A_A = A_B / 2.
Step 3: Substitute the values for wire A into the resistance formula: R_A = ρ(L_A / A_A).
Step 4: Replace L_A and A_A with their expressions in terms of wire B: R_A = ρ((2L_B) / (A_B / 2)).
