Chapter : 1. Electricity
Derivation of mathematical expression of parallel combination
Derivation of mathematical expression of parallel combination :
Let, V be the potential difference across the two common points A and B. Then, from Ohm’s law
Current passing through R1, I1 = V/R1 ...(i)
Current passing through R2, I2 = V/R2 ...(ii)
Current passing through R3, I3 = V/R3 ...(iii)
If R is the equivalent resistance, then from Ohm’s law, the total current flowing through the circuit is given by,
I = V/R ...(iv)
and I = I1 + I2 + I3 ...(v)
Substituting the values of I, I1, I2 and I3 in Equation (v),
= ...(vi)
Cancelling common V term, one gets
The equivalent resistance of a parallel combination of resistance is less than each of all the individual resistances.
Important results about parallel combination :
(i) Total current through the circuit is equal to the sum of the currents flowing through it.
(ii) In a parallel combination of resistors the voltage (or potential difference) across each resistor is the same and is equal to the applied voltage i.e.
i.e. V1 = V2 = V3 = V :
(iii) (iii) Current flowing through each resistor is inversely proportional to its resistances, thus higher the resistance of a resistors, lower will be the current flowing through it.
Let, V be the potential difference across the two common points A and B. Then, from Ohm’s law
Current passing through R1, I1 = V/R1 ...(i)
Current passing through R2, I2 = V/R2 ...(ii)
Current passing through R3, I3 = V/R3 ...(iii)
If R is the equivalent resistance, then from Ohm’s law, the total current flowing through the circuit is given by,
I = V/R ...(iv)
and I = I1 + I2 + I3 ...(v)
Substituting the values of I, I1, I2 and I3 in Equation (v),
= ...(vi) Cancelling common V term, one gets
The equivalent resistance of a parallel combination of resistance is less than each of all the individual resistances.
Important results about parallel combination :
(i) Total current through the circuit is equal to the sum of the currents flowing through it.
(ii) In a parallel combination of resistors the voltage (or potential difference) across each resistor is the same and is equal to the applied voltage i.e.
i.e. V1 = V2 = V3 = V :
(iii) (iii) Current flowing through each resistor is inversely proportional to its resistances, thus higher the resistance of a resistors, lower will be the current flowing through it.
Trending Articles & Blogs
- Physics Tutor, Math Tutor Improve Your Child’s Knowledge
- How to Get Maximum Marks in Examination Preparation Strategy by Dr. Mukesh Shrimali
- 5 Important Tips To Personal Development Apply In Your Daily Life
- Breaking the Barriers Between High School and Higher Education
- 14 Vocational courses after class 12th
- Tips to Get Maximum Marks in Physics Examination
- Get Full Marks in Biology Class 12 CBSE
Download Old Sample Papers For Class X & XII
Download Practical Solutions of Chemistry and Physics for Class 12 with Solutions
Recent Questions Asked
- Newton’s laws of motion asked by Dr. Mukesh Shrimali
- Process of nutrition in Amoeba asked by Rajiv Sharma
- Importance of studying physics subject in school after 10th asked by Rajiv
- Refraction Through Prism in Different Medium asked by Kirti Sharma
- Ratio and Proportion Question asked by Education Desk
- Explain all the 12 tenses with example asked by Qwerty
- Refraction Through Prism in Different Medium asked by Seema Shrimali