Question

Problem 3.1 A. In the circuit at right, use your model for electric current to rank the bulbs according to brightness when the switch is open. Explain your reasoning. B. Rank the bulbs according to brightness when the switch is closed. Explain your reasoning.

Answer 1

Brightness depends on power output of bulb( VxI).
Let Resistance of all Bulbs are equal (Identical Bulb) R_A = R_B = R_C = R A. When switch is open there is no current in B I = I_A = I_C V_A = I_A R_A = IR V_C = I_C R_C = IR Power output: - P_A = V_A I_A = I^2R P_C = V_C I_C = I^2 R P_B = V_C I_B = 0 Brightness of A = Brightness of C and Brightness of B = 0 b. When switch is closed The Equivalent Resistance R_eq = (R_A parallel R_B) + R_C = (R parallel R) + R = R/2 + = 3R/2 V = IR_eq = I3R/2 implies I = 2V/3R from current Division Rule I_a = R_B/R_A + R_B I_C R/R + R 2V/3r = V/3R I_B = R_A/R_A + R_B I = V/3R I_C = I = 2V/3R \r\n Power output P = VI = I^2R because V = IR R_A = I^2_A R_A = (V/3R)^2 R = V^2/9R