An unknown resistor is connected between the terminals of a $3.00 \mathrm{V}$ battery. Energy is dissipated in the resistor at the rate of $0.707 \mathrm{W}$ . The same resistor is then connected between the terminals of a $12.0 \mathrm{V}$ battery. At what rate is energy now dissipated?

In the given figure, a battery of potential difference $V=12 \mathrm{V}$ is connected to a resistive strip of resistance $R=4.0 \mathrm{\Omega }$. When an electron moves through the strip from one end to the other,

$\left(a\right)$ in which direction in the figure do the electrons move 

$\left(b\right)$ how much work is done on the electrons by the electric field in the strip

$\left(c\right)$how much energy is transferred into thermal energy of the strip by the electrons?

A$60 \mathrm{W}$ light bulb is plugged into a standard $120 \mathrm{V}$ outlet. 

$\left(a\right)$ How much does it cost per $31$-day month to leave the light turned on continuously? Assume electrical energy costs $\mathrm{US}\$0.06 \mathrm{per} \mathrm{kWh}.$

$\left(b\right)$ What is the resistance of the bulb?

$\left(c\right)$ What is the current in the bulb?

The figure gives the electric potential $V\left(x\right)$ along a copper wire carrying uniform current, from a point of higher potential $V_1=12.0 \mathrm{\mu V}$ to a point of zero potential at $x_s=3.00 \mathrm{m}$. The wire has a radius of $2.20 \mathrm{mm}$. What is the current in the wire?

A $120 \mathrm{V}$ Potential difference is applied to a space heater whose resistance is $12 \mathrm{\Omega }$ when hot,

$\left(a\right)$ At what rate is electrical energy transferred to thermal energy?
$\left(b\right)$ What is the cost for $5.0 \mathrm{h}$ at $\mathrm{US}\$0.07 \mathrm{per} \mathrm{kWh}?$

If the gauge number of a wire is increased by $6,$ the diameter is halved; if a gauge number is increased by $1,$ the diameter decreases by the factor $2^{\frac{1}{6}}$. Knowing that $1000 \mathrm{ft}.$ of $10$ gauge copper wire has a resistance of approximately $1.00 \mathrm{\Omega }$. Estimate the resistance of $13 \mathrm{ft}.$ of $22$ gauge copper wire.

Swimming during a storm. The figure, given below, shows a swimmer at distance $D=38.0 \mathrm{m}$ from a lightning strike to the water, with current $I=78 \mathrm{kA}$ . The water has resistivity $30 \mathrm{\Omega m}$ . The width of the swimmer along a radial line from the strike is $0.70 \mathrm{m}$, and his resistance across that width is $4.00 \mathrm{k\Omega }$. Assume that the current spreads through the water over a hemisphere centred on the strike point. What is the current through the swimmer?

Wire $C$ and wire $D$ are made from different materials and have length $L_{\mathrm{C}}=L_{\mathrm{D}}=1.0 \mathrm{m}.$ The resistivity and radius of wire $C$ are $2.0\times {10}^{-6} \mathrm{\Omega m}$ and $1.00 \mathrm{mm},$ and those of wire $D$ are $1.0\times {10}^{-6} \mathrm{\Omega m}$ and $0.50 \mathrm{mm}$. The wires are joined as shown in fig. and a current of $2.0 \mathrm{A}$ is set up in them. What is the electric potential difference between
(a) points $1$ and $2$ and (b) points $2$ and $3$ ? What is the rate at which energy is dissipated between (c) points $1$ and $2$ and (d) points $2$ and $3$?