Ohm's Law

Four identical light bulbs, each rated at $U_0 = 12$ V and $P_0 = 24$ W, are connected in parallel and powered by a source with EMF $\varepsilon = 12$ V and internal resistance $r = 0.20\ \Omega$. Assume the filament resistance is constant (independent of current).

In the circuit shown, the voltage between points $a$ and $b$ is $U_{ab} = 9.0$ V. The network has two parallel branches between $a$ and $b$. The first branch is a $2$ k$\Omega$ resistor in series with a $10$ k$\Omega$ resistor. The second branch is a $1$ k$\Omega$ resistor in series with a $5$ k$\Omega$ resistor. (In the figure, "k" denotes kilohms.)

In the circuit shown, $R_1$ and $R_3$ are connected in parallel between the positive terminal of the supply and a middle node; $R_2$ and $R_4$ are connected in parallel between that middle node and the negative terminal. The supply voltage is $U = 6.0$ V. Given $R_1 = 10$ k$\Omega$, $R_2 = 5.0$ k$\Omega$, $R_3 = 2.0$ k$\Omega$, $R_4 = 1.0$ k$\Omega$.

In the circuit shown, a source of EMF $U = 3.0$ V drives two parallel branches. One branch has $R_1$ in series with $R_2$, with point $a$ at the node between them. The other branch has $R_3$ in series with $R_4$, with point $b$ at the node between them. Given $R_1 = R_2$.

A galvanometer has an internal resistance $R_g = 90 \ \Omega$ and a full-scale deflection current $I_g = 0.02 \ \text{A}$.

Two light bulbs are rated <!--LATEXPH0-->'' and $110 \ \text{V}, 40 \ \text{W}$''.

Ten identical storage cells are connected in series. Each cell has EMF $\varepsilon_0 = 2.0 \ \text{V}$ and internal resistance $r_0 = 0.04 \ \Omega$. The series battery group is connected to an external resistor $R = 3.6 \ \Omega$.

Two incandescent bulbs have rated values "$220 \ \text{V}, 100 \ \text{W}$" (bulb $A$) and "$220 \ \text{V}, 60 \ \text{W}$" (bulb $B$). Their voltage--current characteristic curves are given; both curves rise monotonically and bend over (the resistance grows with voltage because the filament heats up).

Representative readings from the curves:

An ohmmeter directly measures resistance and is usually a component of a multimeter. Its construction is shown in figure 13.34(a) and includes a galvanometer, a power source, and a variable resistor. When the red and black probes touch directly, the variable resistor is adjusted so that the galvanometer needle reaches full-scale deflection. The current at this moment is

where $\mathcal{E}$ is the EMF of the source, $r$ is the source's internal resistance, $R_g$ is the galvanometer's internal resistance, and $R$ is the adjusted value of the variable resistor. The sum $(r+R_g+R)$ is called the total internal resistance of the ohmmeter, $R_{\text{total}}$. When the resistance between the probes is zero, the needle points to full scale; when the probes are separated (resistance infinite), $I=0$ and the needle points to zero. When an unknown resistance $R_x$ is connected between the probes,

For a fixed $R_{\text{total}}$, every $R_x$ corresponds to a unique $I$, so resistance values can be marked directly on the galvanometer's scale.

Suppose the scale of a particular ohmmeter is as shown in figure 13.34(b), where arc $AB$ is centered on the needle's pivot. When the probes are separated, the needle points to $A$; when they touch, the needle points to $B$. Point $C$ is the midpoint of arc $AB$; $D$ is the midpoint of arc $AC$; $E$ is the midpoint of arc $AD$; and $F$ is the midpoint of arc $CB$. The total internal resistance is $R_{\text{total}}=4.8\ \text{k}\Omega$, and the galvanometer's deflection angle is proportional to the current (so the current scale is uniform).

Two resistors are given. When they are connected in parallel, the total resistance is $2.4 \ \Omega$. When they are connected in series, the total resistance is $10 \ \Omega$.