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Judge the equivalent resistance when the following are connected in parallel a) 1ohm and 10^6 ohm b) 10^3 ohm and 10^6 ohm
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Judge the equivalent resistance when the following are connected in pa...
Equivalent Resistance in Parallel Connection
Parallel connection refers to the arrangement of electrical components where the ends of each component are connected together at a common point. In this configuration, the voltage across each component is the same, while the current divides among them. To determine the equivalent resistance of components connected in parallel, we use the formula:
1/R_eq = 1/R1 + 1/R2 + ... + 1/Rn
Where R_eq represents the equivalent resistance and R1, R2, ..., Rn are the resistances of the individual components.
a) 1 ohm and 10^6 ohm:
When a 1 ohm resistor and a 10^6 ohm resistor are connected in parallel, we can calculate the equivalent resistance as follows:
1/R_eq = 1/1 + 1/10^6
1/R_eq = 1 + 10^-6
1/R_eq = 1.000001
To find R_eq, we take the reciprocal of both sides:
R_eq = 1/1.000001
R_eq ≈ 0.999999 ohms
Therefore, the equivalent resistance when a 1 ohm resistor and a 10^6 ohm resistor are connected in parallel is approximately 0.999999 ohms.
b) 10^3 ohm and 10^6 ohm:
Let's calculate the equivalent resistance when a 10^3 ohm resistor and a 10^6 ohm resistor are connected in parallel:
1/R_eq = 1/10^3 + 1/10^6
1/R_eq = 10^-3 + 10^-6
1/R_eq = 0.001001
Taking the reciprocal of both sides:
R_eq = 1/0.001001
R_eq ≈ 998.001 ohms
Hence, the equivalent resistance when a 10^3 ohm resistor and a 10^6 ohm resistor are connected in parallel is approximately 998.001 ohms.
Summary:
- When a 1 ohm resistor and a 10^6 ohm resistor are connected in parallel, the equivalent resistance is approximately 0.999999 ohms.
- When a 10^3 ohm resistor and a 10^6 ohm resistor are connected in parallel, the equivalent resistance is approximately 998.001 ohms.
In parallel connections, the equivalent resistance is always smaller than the smallest resistance among the components. It can be observed that when a resistor with a significantly higher resistance is connected in parallel with a lower resistance, the resulting equivalent resistance approaches the value of the lower resistance. This is because the high resistance path allows only a small amount of current to flow, while the low resistance path allows a larger current, resulting in the equivalent resistance being close to the lower value.
Parallel connection refers to the arrangement of electrical components where the ends of each component are connected together at a common point. In this configuration, the voltage across each component is the same, while the current divides among them. To determine the equivalent resistance of components connected in parallel, we use the formula:
1/R_eq = 1/R1 + 1/R2 + ... + 1/Rn
Where R_eq represents the equivalent resistance and R1, R2, ..., Rn are the resistances of the individual components.
a) 1 ohm and 10^6 ohm:
When a 1 ohm resistor and a 10^6 ohm resistor are connected in parallel, we can calculate the equivalent resistance as follows:
1/R_eq = 1/1 + 1/10^6
1/R_eq = 1 + 10^-6
1/R_eq = 1.000001
To find R_eq, we take the reciprocal of both sides:
R_eq = 1/1.000001
R_eq ≈ 0.999999 ohms
Therefore, the equivalent resistance when a 1 ohm resistor and a 10^6 ohm resistor are connected in parallel is approximately 0.999999 ohms.
b) 10^3 ohm and 10^6 ohm:
Let's calculate the equivalent resistance when a 10^3 ohm resistor and a 10^6 ohm resistor are connected in parallel:
1/R_eq = 1/10^3 + 1/10^6
1/R_eq = 10^-3 + 10^-6
1/R_eq = 0.001001
Taking the reciprocal of both sides:
R_eq = 1/0.001001
R_eq ≈ 998.001 ohms
Hence, the equivalent resistance when a 10^3 ohm resistor and a 10^6 ohm resistor are connected in parallel is approximately 998.001 ohms.
Summary:
- When a 1 ohm resistor and a 10^6 ohm resistor are connected in parallel, the equivalent resistance is approximately 0.999999 ohms.
- When a 10^3 ohm resistor and a 10^6 ohm resistor are connected in parallel, the equivalent resistance is approximately 998.001 ohms.
In parallel connections, the equivalent resistance is always smaller than the smallest resistance among the components. It can be observed that when a resistor with a significantly higher resistance is connected in parallel with a lower resistance, the resulting equivalent resistance approaches the value of the lower resistance. This is because the high resistance path allows only a small amount of current to flow, while the low resistance path allows a larger current, resulting in the equivalent resistance being close to the lower value.
Community Answer
Judge the equivalent resistance when the following are connected in pa...
ans is...1/1.001002 i.e approx(0.998ohm)
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Judge the equivalent resistance when the following are connected in parallel a) 1ohm and 10^6 ohm b) 10^3 ohm and 10^6 ohm for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Judge the equivalent resistance when the following are connected in parallel a) 1ohm and 10^6 ohm b) 10^3 ohm and 10^6 ohm covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Judge the equivalent resistance when the following are connected in parallel a) 1ohm and 10^6 ohm b) 10^3 ohm and 10^6 ohm.
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