10 resistors, each of resistance R are connected in series to a battery of emf E and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased n times. The value of n is:
100
1
1000
10
The Correct Option is A
Approach Solution - 1
To find the value of \(n\), the factor by which current increases when the resistors are connected in parallel compared to series, let's analyze both configurations. When resistors are connected in series, the total resistance \(R_s\) is:
\[R_s = 10R\]
The current \(I_s\) through the series circuit connected to a battery of emf \(E\) is given by Ohm's Law:
\[I_s = \frac{E}{R_s} = \frac{E}{10R}\]
For resistors connected in parallel, the total resistance \(R_p\) is:
\[\frac{1}{R_p} = \frac{1}{R} + \frac{1}{R} + \cdots + \frac{1}{R} = \frac{10}{R}\]
Simplifying, we get:
\[R_p = \frac{R}{10}\]
The current \(I_p\) through the parallel circuit is:
\[I_p = \frac{E}{R_p} = \frac{E}{\frac{R}{10}} = \frac{10E}{R}\]
The ratio of currents \(n\) is:
\[n = \frac{I_p}{I_s} = \frac{\frac{10E}{R}}{\frac{E}{10R}} = 100\]
Therefore, the value of \(n\) is 100.
Approach Solution -2
\(I_s=\frac{E}{10R}\) ……….(1)
\(I_p=\frac{E}{\frac{R}{10}}=\frac{10E}{R}\) ……..(2)
According to eq. (1) and (2)
\(n=\frac{I_p}{I_s}=100\)
\(\Rightarrow n=100\)
So, the correct answer is option (A): 100
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Concepts Used:
Resistance
Resistance is the measure of opposition applied by any object to the flow of electric current. A resistor is an electronic constituent that is used in the circuit with the purpose of offering that specific amount of resistance.
R=V/I
In this case,
v = Voltage across its ends
I = Current flowing through it
All materials resist current flow to some degree. They fall into one of two broad categories:
- Conductors: Materials that offer very little resistance where electrons can move easily. Examples: silver, copper, gold and aluminum.
- Insulators: Materials that present high resistance and restrict the flow of electrons. Examples: Rubber, paper, glass, wood and plastic.
Resistance measurements are normally taken to indicate the condition of a component or a circuit.
- The higher the resistance, the lower the current flow. If abnormally high, one possible cause (among many) could be damaged conductors due to burning or corrosion. All conductors give off some degree of heat, so overheating is an issue often associated with resistance.
- The lower the resistance, the higher the current flow. Possible causes: insulators damaged by moisture or overheating.