Answer to Question #124912 in Classical Mechanics for Stefanie Hernandez-Mendez

Question #124912
A battery has an emf of ε = 3 V, an internal resistance r = 29 Ω, and is connected to a resistor of R = 65 Ω.

(a) Express the current I through the circuit in terms of ε, r and R.
b. Calculate the numerical value of I in A.
c. Express the terminal voltage ΔV of the battery in terms of I and R.
d.Calculate the numerical value of ΔV in V.
1
Expert's answer
2020-07-02T17:14:11-0400

Question (a)


Considering that the circuit is a series circuit, the equivalent resistance is


"R_{eq}=r+R"


Applying Ohm's Law you have to


"I=\\frac{V}{R_{eq}}"


Where.

  • The potential difference is "V=\\varepsilon"
  • The equivalent resistance is "R_{eq}=r+R"

The expression of the current is "\\displaystyle \\color{red}{\\boxed{I=\\frac{\\varepsilon}{r+R}}}"


Question (b)


Numerically evaluating the voltage and resistance values


"I=\\frac{3\\;V}{29\\;\\Omega+65\\;\\Omega}=0.032\\;A"


The numerical value of the current is "\\displaystyle \\color{red}{\\boxed{I=0.032\\;A}}"


Question (c)


Applying Ohm's Law, we have that the voltage at the terminals is


"\\Delta V=I\\;R"


Where.

  • The current is "I"
  • The connected resistance is "R"

The expression for the potential difference at the battery terminals is "\\displaystyle \\color{red}{\\boxed{\\Delta V=I\\;R}}"


Question (d)


Numerical evaluation to calculate the potential difference


"\\Delta V=I\\;R"


"\\Delta V=0.032\\;A\\times 65\\;\\Omega=2.08\\;V"


The potential difference at the terminals is "\\displaystyle \\color{red}{\\boxed{\\Delta V=2.08\\;V}}"


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