A wire made of material A has twice the length and half the cross-sectional area
Practice Questions
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
Questions & Step-by-Step Solutions
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?
Correct Answer: 4R_B
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)).
Step 6: Recognize that R_B = ρ(L_B / A_B), so we can express R_A in terms of R_B: R_A = 4 * R_B.
Resistance Calculation – Understanding how to calculate resistance using the formula R = ρ(L/A), where ρ is resistivity, L is length, and A is cross-sectional area.
Proportional Relationships – Recognizing how changes in length and area affect resistance, particularly how doubling length and halving area interact.
