Ask Question
21 July, 20:04

An external resistor with resistance R is connected to a battery that has an emf E and an internal resistance r. Let P be the electrical power output of the source. By conservation of energy, P is equal to the power consumed by R.

(a) What is the value of P in the limit that R is very small?

(b) What is the value of P in the limit that R is very large?

+1
Answers (1)
  1. 21 July, 20:20
    0
    a) When R is very small R << r, therefore the term R + r will equal r and the current becomes

    b) When R is very large, R >> r, therefore the term R + r will equal R and the current becomes

    Explanation:

    Solution:

    (a) We want to get the consumed power P when R is very small. The resistor in the circuit consumed the power from this battery. In this case, the current I is leaving the source at the higher-potential terminal and the energy is being delivered to the external circuit where the rate (power) of this transfer is given by equation in the next form

    P=∈*I-I^2*r (1)

    Where the term ∈*I is the rate at which work is done by the battery and the term I^2*r is the rate at which electrical energy is dissipated in the internal resistance of the battery. The current in the circuit depends on the internal resistance r and we can apply equation to get the current by

    I=∈/R+r (2)

    When R is very small R << r, therefore the term R + r will equal r and the current becomes

    I = ∈/r

    Now let us plug this expression of I into equation (1) to get the consumed power

    P=∈*I-I^2*r

    =I (∈-I*r)

    =0

    The consumed power when R is very small is zero

    (b) When R is very large, R >> r, therefore the term R + r will equal R and the current becomes

    I=∈/R

    The dissipated power due toll could be calculated by using equation.

    P=I^2*r (3)

    Now let us plug the expression of I into equation (3) to get P

    P=I^2*R = (∈/R) ^2*R

    =∈^2/R
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “An external resistor with resistance R is connected to a battery that has an emf E and an internal resistance r. Let P be the electrical ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers