1. A student connects four lamps A, B, C and D in the circuit shown in Figure 1. The battery has an emf of 9.0 mathrm(~V) and negligible internal resistance. Figure 1 (a) The table shows the operating conditions for the lamps when they are at normal brightness. Lamps & Operating voltage mathrm(V) & Power mathrm(W) A and C & 6.0 & 6.0 B and D & 3.5 & 4.1 The student observes that two of the lamps are at their normal brightness. Assume that any changes in resistance of the lamps are negligible. Determine which two lamps are at their normal brightness. Use calculations to support your answer. (b) The student connects another lamp mathbf(E) in the circuit as shown in Figure 2. Lamp mathbf(E) is identical to lamps mathbf(A) and mathbf(C) . Figure 2

Question

1. A student connects four lamps A, B, C and D in the circuit shown in Figure 1. The battery has an emf of 9.0 mathrm(~V) and negligible internal resistance. Figure 1 (a) The table shows the operating conditions for the lamps when they are at normal brightness. Lamps & Operating voltage mathrm(V) & Power mathrm(W) A and C & 6.0 & 6.0 B and D & 3.5 & 4.1 The student observes that two of the lamps are at their normal brightness. Assume that any changes in resistance of the lamps are negligible. Determine which two lamps are at their normal brightness. Use calculations to support your answer. (b) The student connects another lamp mathbf(E) in the circuit as shown in Figure 2. Lamp mathbf(E) is identical to lamps mathbf(A) and mathbf(C) . Figure 2

Answer 1

The lamps B and D are the lamps, which operate at their maximum brightness as the total required voltage accumulates to less than the total provided battery emf, hence ensuring their full operational conditions.

Answer 2

## Step1: Identify the given information The question gives us the following data:Four lamps: A, B, C, and D are connected in a circuit, with Battery having an emf of 9.0 V, negligible internal resistance. The operating voltage and power for Lamps A and C is 6.0 V and 6.0 W respectively. Lamps B and D require operating voltage 3.5 V and power 4.1 W. Our objective for part (a) is to analyze the circuit and identify which two lamps are operating at their normal brightness. Since brightness of the bulb corresponds to the energy it uses to light, therefore the brighter the lamp, the more power it is using.## Step2: Observations and deductions From the above information, bulbs A and C have an operating voltage of 6.0 V each which means if two are in a circuit they will require a total of 6 + 6 = 12.0 V to operate normally, which is more than total provided emf. Hence, bulbs A and C can't operate normally with the 9.0 V battery as they require more voltage. ### Formula used: Sum of voltages for a series circuit _since we don't have the detailed illustration of the circuit's connections. So let's base on the information assumption._ For bulbs B and D, their operating voltage is 3.5 V each. So connecting these two would require: 3.5 + 3.5 = 7.0 VThis is less than the total 9.0 provided by the battery, so B and D can operate at their maximum brightness there as they achieve their operable voltage. ## Step3: Conclude part (a)Based on these simple voltage addition calculations, we can conclude lamps B and D could operate at normal brightness in a described circuit diagram._(The answer to problem (b) isn't requested in the original problem instruction metric.)_

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