In the diagram above, the voltage difference between a and b is 6V. If R₁ = 25 Ω, R₃ = 45 Ω, and I = 0.095 A, then find R₂.

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Using Ohm's Law, we can find the voltage drop across each resistor: - Voltage drop across R₁: V1 = IR1 = (0.095 A)(25 Ω) = 2.375 V - Voltage drop across R₃: V2 = IR2 = (0.095 A)(45 Ω) = 4.275 V Since the voltage difference between a and b is 6V, the voltage drop across R₂ (let's call it V3) is: V3 = (Voltage difference between a and b) - (V1 + V2) = 6 V - (2.375 V + 4.275 V) = -0.65 V Wait, that can't be right. A voltage drop can't be negative! This means that our assumption that the current flows from a to b may be incorrect. Let's assume that the current actually flows from b to a and try again: - Voltage drop across R₁: V1 = IR1 = (0.095 A)(25 Ω) = 2.375 V - Voltage drop across R₃: V2 = IR2 = (0.095 A)(45 Ω) = 4.275 V Since the voltage difference between a and b is 6V, the voltage drop across R₂ (let's call it V3) is: V3 = (Voltage difference between b and a) - (V1 + V2) = -6 V - (2.375 V + 4.275 V) = -12.65 V Finally, we can use Ohm's Law to find R₂: V = IR, so R = V/I R of R₂ = V3/I = (-12.65 V)/(0.095 A) = -133 Ω Oh no, another negative value! This means that our assumption that the current flows from b to a and that the voltage difference between a and b is 6V is incorrect. There is no resistor value that can satisfy the given conditions.

In the Diagram Above, the Voltage Difference Between a and B