36 In the given circuit, A, B, C and D are four lamps connected with a battery of

60V.

Analyse the circuit to answer the following questions.

(i) What kind of combination are the lamps arranged in (series or parallel)?

(ii) Explain with reference to your above answer, what are the advantages (any

two) of this combination of lamps?

(iii) Explain with proper calculations which lamp glows the brightest?

(iv) Find out the total resistance of the circuit.

A parallel circuit, is one which the conductors leading into the bulbs are joined together on one side of the bulbs, and the conductors coming out of the bulbs are joined together on the other side of the bulb

The correct arrangement, advantages, lamp and resistance values are;

(i) The lamps are arranged in parallel

(ii) Improved reliability

Optimum performance of the bulbs

(iii) Lamp C

(iv) The total resistance is 4 Ω

The reason the above values are correct are as follows:

(i) From the diagram attached, the lamps are arrange in parallel

This is so because, each lamp is directly connected across the terminals of the the voltage source

(ii) The advantages of the bulbs arranges in parallel are;

The other lamps will continue working if one lamp becomes faulty

The voltage is applied directly to each lamp, such that the lamps are lit with the maximum power available in the circuit

(iii) The brightness of the lamp is given by the power of the lamp

The lamp with the highest wattage, or power glows the most

Power, P = Voltage, V × Current, I

The power for lamp A, [tex]P_A[/tex] = 60 V × 3 A = 180 W

The power for lamp B, [tex]P_B[/tex] = 60 V × 4 A = 240 W

The power for lamp C, [tex]P_C[/tex] = 60 V × 5 A = 300 W (Brightest)

The power for lamp D, [tex]P_D[/tex] = 60 V × 3 A = 180 W

Therefore, lamp C has the highest power and glows the brightest

(iv) The total resistance is given by the voltage, divided by the total current

Total current, I = 3 A + 4 A + 5 A + 3 A = 15 A

[tex]Total \ resistance, \ R_{tot} = \dfrac{V}{I_{tot}}[/tex]

Therefore;

[tex]Total \ resistance, \ R_{tot} = \dfrac{60 \, V}{15 \, A }}=4 \, \Omega[/tex]

The total resistance, R = 4 Ω

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