In Figure ,${\mathbf{R}}_1\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{V}$ , ${\mathbf{R}}_2\mathbf{=}\mathbf{18}\mathbf{.}\mathbf{0}\mathbf{V}$and the ideal battery has emf $\mathbf{\epsilon }\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{V}$.

(a) What is the size of current $\mathbf{}{\mathbf{i}}_1$?

(b) What is the direction (left or right) of current $\mathbf{}{\mathbf{i}}_1$ ?

(c) How much energy is dissipated by all four resistors in 1.00 min?

You are to connect resistors R1 and R2, with $\mathbf{R}\mathbf{1}\mathbf{>}\mathbf{R}\mathbf{2}$, to a battery, first individually, then in series, and then in parallel. Rank those arrangements according to the amount of current through the battery, greatest first.

In Fig. $\mathbf{\text{27-33,}}$Battery 1 has emf V and internal resistance $\mathbf{r}\mathbf{1}\mathbf{\text{=0.016}}$ and battery 2 has emf V and internal resistance $\mathbf{r}\mathbf{2}\mathbf{=}\mathbf{\text{0.012.}}$ The batteries are connected in series with an external resistance R.

(a) What R-value makes the terminal-to-terminal potential difference of one of the batteries zero?

(b) Which battery is that?

A capacitor with an initial potential difference of$\mathbf{100}\mathit{V}$ is discharged through a resistor when a switch between them is closed at$\mathbf{t}\mathbf{=}\mathbf{0}$. At$\mathit{t}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{0}\mathit{s}$, the potential difference across the capacitor is$\mathbf{1}\mathbf{.}\mathbf{00}\mathit{V}$. (a) What is the time constant of the circuit? (b) What is the potential difference across the capacitor at$\mathbf{t}\mathbf{=}\mathbf{17}\mathbf{.}\mathbf{0}\mathbf{s}$?

(a) In Fig. 27-18a, are resistors $\mathbf{}{\mathbf{R}}_1$ and ${\mathbf{R}}_3$in series?

(b) Are resistors $\mathbf{}{\mathbf{R}}_1\mathbf{\&}\mathbf{}{\mathbf{R}}_3$in parallel?

(c) Rank the equivalent resistances of the four circuits shown in Fig. 27-18, greatest first.

Figure 27-78 shows a portion of a circuit through which there is a current I=6.00A . The resistances are R₁.=R₂ =2.00R₃ =2.OOR₄ =4.00$\Omega$What is the current i₁ through resistor 1?