The Ammeter and the Voltmeter

The ideal battery in the given figure (a) has emf $\mathcal{E}=10.0 \mathrm{V}$. Plot $1$ in the figure (b) gives the electric potential difference $V$ that can appear across resistor 1 versus the current $i$ in that resistor when the resistor is individually tested by putting a variable potential across it. The scale of the $V$ axis is set by $V_s=18.0 \mathrm{V}$, and the scale of the $i$ axis is set by $i_s=3.00 \mathrm{mA}$. Plots $2$ and $3$ are similar plots for resistors $2$ and $3$, respectively, when they are individually tested by putting a variable potential across them. What is the current in resistor $2$ in the circuit of figure a?

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

A $5.0 \mathrm{km}$ long underground cable extends east to west and consists of two parallel wires, each of which has resistance $13 \mathrm{\Omega } {\mathrm{km}}^{-1}$. An electrical short develops at distance $x$ from the west end when a conducting path of resistance $R$ connects the wires as shown in the figure. The resistance of the wires and the short is then $100 \mathrm{\Omega }$ when measured from the east end and $200 \mathrm{\Omega }$ when measured from the west end. What are (a) $x$ and (b) $R$?

In the figure, $R_1=R_2=4.00 \mathrm{\Omega }$ and $R_3=1.50 \mathrm{\Omega }$. Find the equivalent resistance between points $D$ and $E$.

A car battery with a $12 \mathrm{V}$ emf and an internal resistance of $0.030 \mathrm{\Omega }$ is being charged with a current of $40 \mathrm{A}$. What are (a) the potential difference $V$ across the terminals, (b) the rate $P_r$ of energy dissipation inside the battery, and (c) the rate $P_{\mathrm{emf}}$ of energy conversion to chemical form? When the battery is used to supply $40 \mathrm{A}$ to the starter motor, what are (d) $V$ and (e) $P_r$?

(a) In Fig, what value must $R$ have if the current in the circuit is to be $1.5 \mathrm{mA}$ ? Take ${\mathcal{E}}_1=2.0 \mathrm{V}, {\mathcal{E}}_2=3.0 \mathrm{V}$, and $r_1=r_2=3.0 \mathrm{\Omega }$
(b) What is the rate at which thermal energy appears in $R$?

In Fig., $R_1=6.00 \mathrm{\Omega }, R_2=24.0 \mathrm{\Omega }$, and the ideal battery has emf $\mathcal{E}=12.0 \mathrm{V}$. What are the (a) size and (b) direction (left or right) of current $i_1$? (c) How much energy is dissipated by all four resistors in $1.00$ min?

When resistors $1$ and $2$ are connected in series, the equivalent resistance is $20.0 \mathrm{\Omega }$. When they are connected in parallel, the equivalent resistance is $3.75 \mathrm{\Omega }$. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

The figure indicates one reason why no one should stand under a tree during a lightning storm. If lightning comes down the side of the tree, a portion can jump over to the person, especially if the current on the tree reaches a dry region on the bark and thereafter must travel through air to reach the ground. In the figure, a part of the lightning jumps through distance $d$ in the air and then travels through the person (who has negligible resistance relative to that of air because of the highly conducting salty fluids within the body). The rest of the current travels through the air alongside the tree, for a distance $h$ If $\frac{d}{h}=0.380$ and the total current is $I=4000 \mathrm{A}$, what is the current through the person?