To apply Problem-Solving Strategy 21.2 Inductors in circuits. Consider the circu

Question

To apply Problem-Solving Strategy 21.2 Inductors in circuits. Consider the circuit in the diagram, containing two identical resistors, RA and RB, of resistance R = 200 ohm , an inductor of inductance L = 260mH, and a voltage source with potential difference V = 10.0V. (Figure 1) At some time t after the switch is closed, the current through point B is IB = 9.00mA . At this time, what is the rate of change delta IB/ delta t of the current through point B? As an circuit analysis, getting the signs right is some times more challenging than understanding the principles. Carefully review the sign rules for the potential difference across an inductor In Kirchhoff's loop rule, when current goes through an inductor in the same direction as the assumed current, it encounters a voltage drop equal to L delta I/delta t, so the corresponding term in the loop equation is - L delta I/delta t. Before writing any equations, organize your information and draw appropriate diagrams. Which of the following are known quantities and those easily calculated through Ohm's law at time t? Be careful not to include quantities found using Kirchoffs Laws Check all that apply. potential difference across the voltage source potential difference across the resistor next to point A potential difference across the resistor next to point B potential difference across the inductor Now that you've set up the problem, choose appropriate equations and solve for your unknowns. Find the value of delta IB/delta t at time t. Express your answer in amperes per second to three significant figures. delta IB/delta t =

Explanation / Answer

At this time,t voltage across inductor L is given by L * delta I_b / delta t , but we know currrent I_b=9mA . Hence V_L = V - I_b*R_b = 10 - 9*0.2= 8.2 hence, delta I_b / delta t = 8.2 / 0.26 =31.54 A/s

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