Ohm's law:

$\overline{){\mathbf{V}}{\mathbf{=}}{\mathbf{i}}{\mathbf{R}}}$

The power dissipated in DC circuits:

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{i}}{\mathbf{V}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{i}}}^{{\mathbf{2}}}{\mathbf{R}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{V}}}^{{\mathbf{2}}}{\mathbf{/}}{\mathbf{R}}}$

**Part A**

We are asked to determine the current in the circuit.

Emf of the battery is equal to the sum of potential difference across all resistive elements of the circuit.

ε = ir_{int} + iR = i(r_{int} + R)

To understand how to compute power dissipation in a resistive circuit.

(Figure 1) The circuit in the diagram consists of a battery with EMF E, a resistor with resistance *R*, an ammeter, and a voltmeter. The voltmeter and the ammeter (labeled V and A) can be considered ideal; that is, their resistances are infinity and zero, respectively. The current in the resistor is *I*, and the voltage across it is *V*. The internal resistance of the battery *r*_{int} is not zero.

**Part A. **What is the ammeter reading *I*? Express your answer in terms of ε, *R*, and *r*_{int}.

**Part B. **What is the voltmeter reading *V*? Express your answer in terms of ε, *R*, and *r*_{int}.

In the following parts, you will express the power dissipated in the resistor of resistance *R* using three different sets of variables.

**Part C. **What is the power *P** _{R}* dissipated in the resistor? Express your answer in terms of

**Part D. **Again, what is the power *P** _{R}* dissipated in the resistor? This time, express your answer in terms of one or more of the following variables:

**Part E. **For the third time, what is the power *P** _{R}* dissipated in the resistor? Express your answer in terms of one or more of the following variables: ε,

**Part F. **What is the total power *P*_{total} dissipated in the resistive elements of the circuit? Express your answer in terms of one or more of the following variables: ε, *r*_{int}, and *R*.

**Part G. **What is the total power *P*_{total} dissipated in the resistive elements of the circuit, in terms of the EMF ε of the battery and the current in the circuit? Express your answer in terms of ε and the ammeter current *I*.

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