Parallel Combination of Resistances: Understanding Brightness in Circuits
What is a parallel combination of resistances?
A) The 20 Ohm light bulb will have the same voltage drop as the 10 Ohm light bulb.
B) The 20 Ohm light bulb will have the same amount of brightness (i.e. power dissipation) as the 10 Ohm light bulb.
C) The 20 Ohm light bulb will be brighter than the 10 Ohm light bulb.
D) The 10 Ohm light bulb will be brighter than the 20 Ohm light bulb.
E) The above statements a) and b) are both correct.
The 10 Ohm light bulb will be brighter than the 20 Ohm light bulb. The correct statement is option is B.
Answer:
When two resistors are placed in parallel, they have the same voltage drop across them. This is because the voltage across each branch of a parallel circuit is the same, and the two light bulbs are in separate branches. Therefore, the 20 Ohm light bulb and the 10 Ohm light bulb will have the same voltage drop across them.
However, since the 10 Ohm light bulb has a lower resistance than the 20 Ohm light bulb, it will draw more current than the 20 Ohm light bulb. This means that the 10 Ohm light bulb will dissipate more power (i.e. be brighter) than the 20 Ohm light bulb.
This is because the power dissipated by a resistor is proportional to the current squared and the resistance. Since the current through the 10 Ohm light bulb is greater than the current through the 20 Ohm light bulb, it will dissipate more power and be brighter.
Therefore, statement b) is correct and the correct answer is "The 10 Ohm light bulb will be brighter than the 20 Ohm light bulb."
Understanding Parallel Combination of Resistances
A parallel combination of resistances is a circuit configuration in which two or more resistors are connected in parallel with each other, so that the current flowing through the circuit is split between the resistors. In a parallel circuit, the resistors are connected across the same two points, and the voltage across each resistor is the same.
When two resistors are placed in parallel, they have the same voltage drop across them. This is because the voltage across each branch of a parallel circuit is the same, and the two light bulbs are in separate branches. Therefore, the 20 Ohm light bulb and the 10 Ohm light bulb will have the same voltage drop across them.
However, since the 10 Ohm light bulb has a lower resistance than the 20 Ohm light bulb, it will draw more current than the 20 Ohm light bulb. This means that the 10 Ohm light bulb will dissipate more power (i.e. be brighter) than the 20 Ohm light bulb.
This is because the power dissipated by a resistor is proportional to the current squared and the resistance. Since the current through the 10 Ohm light bulb is greater than the current through the 20 Ohm light bulb, it will dissipate more power and be brighter.
Therefore, statement b) is correct and the correct answer is "The 10 Ohm light bulb will be brighter than the 20 Ohm light bulb."
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