Thermal energy is to be generated in a $\mathbf{0}\mathbf{.10}\mathbf{}\mathbf{\text{\hspace{0.17em}Ω}}$resistor at the rate of $\mathbf{10}\mathbf{}\mathbf{\text{W}}$by connecting the resistor to a battery whose emf is$\mathbf{1}\mathbf{.5}\mathbf{}\mathbf{\text{V}}$. (a) What potential difference must exist across the resistor? (b) What must be the internal resistance of the battery?

Two identical batteries of emf $\mathit{\epsilon }\mathbf{=}\mathbf{12}\mathbf{.0}\mathbf{\text{V}}$ and internal resistance $\mathit{r}\mathbf{=}\mathbf{0}\mathbf{.200}\mathit{\Omega }$are to be connected to an external resistance$\mathit{R}$ , either in parallel (Figure a) or in series (Figure b). (a) If ,$\mathit{R}\mathbf{=}\mathbf{2}\mathbf{.00}\mathit{r}$ what is the current in the external resistance in the parallel arrangement? (b) If $\mathit{R}\mathbf{=}\mathbf{2}\mathbf{.00}\mathit{r}$, what is the current $\mathit{i}$ in the external resistance in the series arrangements? (c) For which arrangement is$\mathit{i}$ greater? (d) If$\mathbf{}\mathit{R}\mathbf{=}\mathit{r}\mathbf{/}\mathbf{2}\mathbf{.00}$ , what is in the external resistance in the parallel? (e) If $\mathbf{}\mathit{R}\mathbf{=}\mathit{r}\mathbf{/}\mathbf{2}\mathbf{.00}$, what is $i$ in the external resistance in the series arrangements? (f) For which arrangement is $i$ greater now?

A simple ohmmeter is made by connecting a $\mathbf{1}\mathbf{.50}\mathbf{\text{\hspace{0.17em}V}}$ flashlight battery in series with a resistance $\mathbf{\text{R}}$ and an ammeter that reads from 0 to $\mathbf{1.00}\mathbf{\text{\hspace{0.17em}mA}}$, as shown in Fig. 27-59. Resistance $\mathbf{\text{R}}$ is adjusted so that when the clip leads are shorted together, the meter deflects to its full-scale value of $\mathbf{1}\mathbf{.00}\mathbf{}\mathbf{\text{mA}}$. What external resistance across the leads results in a deflection of (a) $\mathbf{10.0}\mathit{\%}$, (b) $\mathbf{50.0}\mathit{\%}$, and (c) $\mathbf{90.0}\mathit{\%}$of full scale? (d) If the ammeter has a resistance of $\mathbf{20.0}\mathbf{}\mathbf{\text{Ω}}$and the internal resistance of the battery is negligible, what is the value of $\mathbf{\text{R}}$?

Question: In Figure, the resistances are ,${\mathbf{R}}_{\mathbf{1}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{\Omega }$ ,${\mathbf{R}}_{\mathbf{2}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\Omega }$ and the battery is ideal. What value of R₃ maximizes the dissipation rate in resistance 3?

In Figure,${\mathit{R}}_{\mathbf{1}}\mathbf{=}\mathbf{100}\mathbf{\text{\hspace{0.17em}Ω}}$ , ${\mathit{R}}_{\mathbf{2}}\mathbf{=}\mathbf{50}\mathbf{\text{\hspace{0.17em}Ω}}$, and the ideal batteries have emfs $\mathbf{}{\mathit{\epsilon }}_{\mathbf{1}}\mathbf{=}\mathbf{6}\mathbf{.0}\mathbf{\text{\hspace{0.17em}V}}$,$\mathbf{}{\mathit{\epsilon }}_{\mathbf{2}}\mathbf{=}\mathbf{5}\mathbf{.0}\mathbf{\text{\hspace{0.17em}V}}$ , and .${\mathit{\epsilon }}_{\mathbf{3}}\mathbf{=}\mathbf{4}\mathbf{.0}\mathbf{\text{\hspace{0.17em}V}}$ Find

(a) The current in resistor 1,

(b) The current in resistor 2, and

(c) The potential difference between points a and b.

A 5.0 A current is set up in a circuit for 6.0 min by a rechargeable battery with a 6.0 V emf. By how much is the chemical energy of the battery reduced?