a) Calculate the effective resistance of bulbs A and B. b) Switch S is now closed for a short time. Determine the reading on: Voltmeter V1, Voltmeter V3

QUESTION 1 a) Calculate the effective resistance of bulbs A and B. Step 1: Identify the connection type and resistances. Bulbs A and B are connected in parallel. Resistance of bulb A, R_A = 2 \, . Resistance of bulb B, R_B = 2 \, . Step 2: Use the formula for parallel resistors. (1)/(R_AB) = (1)/(R_A) + (1)/(R_B) Step 3: Substitute the values and calculate R_AB. (1)/(R_AB) = (1)/(2 \, ) + (1)/(2 \, ) (1)/(R_AB) = (2)/(2 \, ) (1)/(R_AB) = (1)/(1 \, ) R_AB = 1 \, The effective resistance of bulbs A and B is 1 \, b) Switch S is now closed for a short time. Determine the reading on: • Voltmeter V1 Step 1: Identify what V1 measures. Voltmeter V1 measures the total electromotive force (EMF) of the battery. There are 4 cells connected in series, and each cell has an EMF of 1.5 V. Step 2: Calculate the total EMF. Total EMF = 4 × 1.5 \, V = 6 \, V The reading on Voltmeter V1 is 6 \, V • Voltmeter V3 Step 1: Calculate the total resistance of the circuit. The parallel combination of A and B (R_AB = 1 \, ) is in series with bulb C (R_C = 3 \, ). R_total = R_AB + R_C R_total = 1 \, + 3 \, = 4 \, Step 2: Calculate the total current in the circuit. Using Ohm's Law, I_total = Total EMFR_total. I_total = 6 \, V4 \, = 1.5 \, A Step 3: Calculate the voltage across bulb C (reading on V3). Using Ohm's Law, V_3 = I_total × R_C. V_3 = 1.5 \, A × 3 \, = 4.5 \, V The reading on Voltmeter V3 is 4.5 \, V c) Calculate the energy transferred in bulb C in 3 seconds if the current in the circuit is 2 A. Step 1: Identify the given values. Current, I = 2 \, A. Time, t = 3 \, s. Resistance of bulb C, R_C = 3 \, . Step 2: Use the formula for energy transferred. E = I^2 R_C t Step 3: Substitute the values and calculate the energy. E = (2 \, A)^2 × 3 \, × 3 \, s E = 4 \, A^2 × 3 \, × 3 \, s E = 36 \, J The energy transferred in bulb C is $*36 \,