If R = 2.0 kΩ,C = 4.0 mF,ε = 8.0 V,Q = 20 mC,and I = 3.0 mA,what is the potential difference V_b − V_a? A)+7.0 V B)+19 V C)+9.0 V D)−3.0 V E)−14 V

Question

Quizplus · Accepted Answer

Using the formula for the potential difference across a capacitor, we have: V = Q/C Plugging in the given values, we get: V = (20 mC)/(4.0 mF) V = 5.0 V This potential difference is shared between the two capacitors in the circuit. Using Kirchhoff's voltage law, we can find the potential difference between the two points as: V_b − V_a = ε - V = 8.0 V - 5.0 V = +3.0 V However, note that the question asks for the opposite of this potential difference, so we have: V_a - V_b = -3.0 V Finally, we can use the formula for the potential difference across a resistor to find the potential difference across R: VR = IR = (2.0 kΩ)(3.0 mA) VR = 6.0 V This potential difference is in the same direction as the potential difference we just found, so we can add them to get the total potential difference: V_a - V_b + VR = -3.0 V + 6.0 V = +3.0 V However, again note that the question asks for the opposite of this potential difference, so we have: V_b - V_a = -3.0 V Therefore, the potential difference between the two points is -3.0 V or +9.0 V depending on the direction chosen. However, since the question asks for the potential difference from point b to point a, the answer is +9.0 V.

If R = 20 KΩ,C = 4