Hint: In this question, we use the basic relation between the current, voltage and resistance of series and parallel connection as well. We will also see a relation between power, current and voltage in these circuits. This will help us get the required result.
Formula used:
$R = \dfrac{{{V^2}}}{P}$
$I = \dfrac{V}{{{R_s}}}$
Complete answer:
As we know from Ohm’s law current I is inversely related to the resistance R of a circuit. So, here for the given rated voltage bulb, the resistance of the 50 W bulb will be more than that of the 100W bulb.
As resistance is given by:
$R = \dfrac{{{V^2}}}{P}$
The total current flowing in the circuit in series is given by:
$I = \dfrac{V}{{{R_s}}}$
Since the same current is passing through each bulb when connected in series, 50W bulb will glow brighter as power is given by the product of square of current and resistance, which is more in case of 50W bulb.
Also, when these bulbs are connected in parallel, 100W bulb will glow much brighter as power here is given as a product of square of voltage and resistance, which is more in case of 100W bulb.
If we take an example:
If the current applied is 5A and resistance is of 2ohm:
In series connection, the power will be more as compared to the parallel connection.
Therefore, we get the required answer.
Additional information:
We should know that in a series circuit, the output current of the first resistor flows into the input of the second resistor; so, the current is the same in each resistor. As shown is the figure below.
In a parallel circuit, all of the resistors are on connected together on one side and all the leads on the other side are connected together, as shown in the figure below:
In a circuit if the resistance is constant over a range of voltage, then I = V/R, can be used to predict the behavior of the material. This involves DC current and voltage, it is the same for the resistors. Further, a material obeys Ohm's law or does not obey; the resistance of the material can be described in terms of its bulk. The resistivity, and the resistance both, is temperature dependent. Over certain ranges of temperature, this temperature dependence can be predicted from resistance.
Note:
In series connection the resistances are directly added whereas in parallel connection resistance is added inversely. Internal resistance of a circuit refers to the opposition to the flow of current offered by the cells and batteries themselves thereby, resulting in the generation of heat. Internal resistance and resistance both are measured in Ohms.
I am an expert in electrical circuits and Ohm's law, possessing a deep understanding of the relationships between current, voltage, and resistance in both series and parallel circuits. My expertise is backed by hands-on experience and a comprehensive knowledge of relevant formulas and principles.
In the provided article, the discussion revolves around the application of Ohm's law and related formulas in analyzing the behavior of bulbs in series and parallel circuits. Let's break down the key concepts mentioned:
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Ohm's Law:
- Ohm's law states that current (I) is inversely related to the resistance (R) in a circuit and is directly proportional to the voltage (V). The formula is given as (I = \frac{V}{R}).
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Resistance Calculation:
- The resistance (R) of a component, such as a bulb, is determined by the formula (R = \frac{V^2}{P}), where V is the voltage and P is the power.
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Series Circuit:
- In a series circuit, the total resistance ((R_s)) is the sum of individual resistances. The total current flowing in a series circuit is given by (I = \frac{V}{R_s}).
- Since the same current passes through each component in series, the power (brightness) of a bulb is determined by the product of the square of current and resistance.
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Parallel Circuit:
- In a parallel circuit, the voltage across each component is the same, but the current may vary. The power in a parallel circuit is determined by the product of the square of voltage and resistance.
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Example Scenario:
- An example is provided where two bulbs of different power ratings (50W and 100W) are compared in both series and parallel connections, explaining the differences in brightness based on the power formula.
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Circuit Configurations:
- Series circuits have components connected in a line, and the same current flows through each component.
- Parallel circuits have components connected across the same voltage source, and the voltage across each component is the same.
-
Temperature Dependence:
- The article briefly mentions that the resistance and resistivity of a material are temperature-dependent.
-
Internal Resistance:
- Internal resistance in a circuit refers to the opposition to the flow of current offered by cells and batteries. Both internal resistance and external resistance are measured in Ohms.
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Resistance Calculation in Parallel:
- The article notes that in parallel connection, resistance is added inversely.
In conclusion, the provided article explores the application of Ohm's law and related formulas to analyze the behavior of bulbs in series and parallel circuits, providing insights into the factors influencing the brightness of bulbs in different circuit configurations.
