Question

In the circuit in the figure, a battery supplies Vemf-23.0 V and R1-8.00 Ω, R2-6.00 Ω, and L-4.00 H. Calculate each of the following a long time after the switch is closed: a) the magnitude of the current flowing out of the battery? 6.708 A emf Computer's answer now shown above. Tries 0/5 b) the magnitude of the current through R1 2.875 A Computer's answer now shown above. Tries 0/5 c) the magnitude of the current through R2 3.833 A Computer's answer now shown above. Tries 0/5 d) the magnitude of the potential difference across R1 23.000 V Computer's answer now shown above. Tries 0/5 e) the magnitude of the potential difference across R2 23.000 V Computer's answer now shown above. Tries 0/5 f) the magnitude of the potential difference across L 0.000V Computer's answer now shown above. Tries 0/5 g) the rate of current change across R1 0.000 A/s Computer's answer now shown above. Tries 0/5

Answer 1

V_emf = 23.0V, R_1 = 8.00 Ohm, R_2 = 6.00 Ohm L = 4.00H At time t = infinity,(along time after the switch is closed) currents are not changing and the circuit is in steady state d_i1/dt = 0, d_i2/dt = 0 d_i1/dt = 0. Rate of change of current Through R_1 is 0 Magnitude of potential difference across L is L d_i2/dt = 0 as d_i2/dt = 0 V_emf = i_1R_1 = i_2R_2 Magnitude of potential difference across R_2 = i_2R_2 = V_emf = 23.0V Magnitude of potential difference across R_1 = i_1R_1 = V_emf = 23.0V Magnitude of current through R_2, i_2 = V_emf/R_2 i_2 = 23.0/6.00 = 3.83A \r\n Magnitude of current through R_1, i_1 = V_emf/R_1 i_1 = 23.0/8.00 = 2.875A Magnitude of current through the battery i = i_1 + i_2 = 6.708A