Two similar cells are used to light two similar lamps as illustrated in the diagrams above. In which of the circuit diagrams are the lamps brightest?

Nnamdium

5 years ago

In series and parallel connection of identical electrical loads, in this case light bulbs, the bulbs when connected in parallel will consume more power than when they are connected in series. This is because when connected in parallel, the effective resistance of the circuit is decreased resulting to more current flow and more power consumption than when connected in series. Also, the voltage across each of the bulbs is same as the the supply voltage, unlike in series connection where each blub will get only half of the supply voltage (since they are identical).

Mathematically,

Let each cell voltage V = 12V, hence, total supply voltage = 24 V
and each bulb has a resistance R = 10 Ohms

FOR SERIES CONNECTION:
V = (E1 + E2) = 24V,
Effective Resistance R = R1 + R2 = 10 + 10 = 20 Ohms
Hence, current flowing through each bulb I = V/R = 24/20 = 1.2A
Power dissipated in each bulb P = I²R = (1.2²) * 10 = 14.4 Watts

FOR PARALLEL CONNECTION:
V = 24V
Effective circuit resistance R = (R1R2)/(R1 + R2) = 100/20 = 5 Ohms
Effective current flowing through the circuit I = V/R = 24/5 = 4.8 A
Current flowing through each bulb will be half of the effective current, i.e. 4.8/2 = 2.4 A,
Hence the power dissipated in each light bulb will be P = I²R = 2.4² * 10 = 5.76 * 10 = 57.6 Watts.

In conclusion, since the brightness of a bulb is proportional to the power it dissipates it implies that the bulbs will shine brighter when connected in parallel.

So, the correct answer should be Option B. (i.e. diagram Q)

favourinchrist

5 years ago

Parallel connection result to low resistance and d voltage must be connected in series to yield brightest lamb

Nnamdium

4 years ago

The explanation for the answer does not agree with the chosen option. Since lower resistance implies higher power, circuit Q, having a lower resistance than P would have higher power, hence higher brightness.