Final answer:
In this case, the first resistor has diameter d, and the second resistor has diameter 2d. If the same current flows through both, the voltage across the two resistors will be: V₁ < V₂
The answer is option ⇒1.
Step-by-step explanation:
When the same current flows through both resistors, we can compare the voltage across the two resistors based on their dimensions.
1) The voltage across a resistor is determined by Ohm's Law, which states that V = IR, where V is the voltage, I is the current, and R is the resistance.
2) The resistance of a cylindrical resistor is given by the formula R = ρ(L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.
3) The cross-sectional area of a cylindrical resistor is proportional to the square of its diameter (A ∝ d²).
4) Let's compare the resistance of the two resistors:
- - For the first resistor with diameter d, its cross-sectional area is A₁ = π(d/2)² = πd²/4.
- - For the second resistor with diameter 2d, its cross-sectional area is A₂ = π(2d/2)² = π(2d)²/4 = π(4d²)/4 = πd².
- - Since the resistors are made of the same material and have equal lengths, their resistivities and lengths cancel out when comparing their resistances.
5) Comparing the resistances, we find that R₁/R₂ = (ρ(L/A₁))/(ρ(L/A₂)) = (πd²/4)/(πd²) = 1/4.
6) Since the current is the same for both resistors, according to Ohm's Law (V = IR), the voltage across a resistor is directly proportional to its resistance.
7) Since the resistance of the first resistor is 1/4 times the resistance of the second resistor, the voltage across the first resistor (V₁) will also be 1/4 times the voltage across the second resistor (V₂).
Therefore, the correct answer is: V₁ < V₂
The answer is option ⇒1
Your question is incomplete, but most probably the full question was:
Two Resistors 1 2 Two cylindrical resistors are made from the same material and are equal in length. The first resistor has diameter d, and the second resistor has diameter 2d.
1) If the same current flows through both, compare the voltage across the two resistors:
Options
- V₁ < V₂
- V₁ = V₂
- V₁ > V₂