Ohm's Law

A battery (EMF $\varepsilon$, internal resistance $r$) is in series with an ideal ammeter, forming the middle branch. Two additional branches are in parallel with this source branch: branch 1 contains $R_1 = 14.0 \Omega$ in series with switch $S_1$; branch 2 contains $R_2 = 9.0 \Omega$ in series with switch $S_2$. When only $S_1$ is closed, the ammeter reads $I_1 = 0.20 A$. When only $S_2$ is closed, it reads $I_2 = 0.30 A$.

In the circuit shown, the source has EMF $\varepsilon = 3$ V and internal resistance $r = 0.6\ \Omega$. The resistors satisfy $R_1 = R_2 = R_3 = 4\ \Omega$ and $R_4 = R_5 = 2\ \Omega$. Between the two terminal rails of the source, two horizontal branches are connected in parallel: the upper branch contains $R_4$ and $R_5$ in series, and the lower branch contains $R_1$, $R_2$, and $R_3$ in series. An ideal ammeter (A) is in the main line in series with the source, and an ideal voltmeter (V) is connected across the parallel combination (i.e., across the upper $R_4$–$R_5$ branch).

In the circuit shown, $C_1 = 6\ \mu\text{F}$, $C_2 = 3\ \mu\text{F}$, $R_1 = 6\ \Omega$, $R_2 = 3\ \Omega$, and a steady source provides $U = 18$ V between the left and right terminals. The upper branch (from the left terminal to the right terminal) consists of $C_1$ in series with $R_2$, with the junction labeled $A$. The lower branch consists of $R_1$ in series with $C_2$, with the junction labeled $B$. A switch $S$ is connected between $A$ and $B$.

Four identical batteries (each with EMF $\varepsilon$ and internal resistance $r$) supply the same load resistor $R$. Three arrangements are considered:

(a) Two parallel branches, each containing $2$ batteries in series. (b) All $4$ batteries connected in series. (c) All $4$ batteries connected in parallel.

Two resistors $R_1 = 2 k\Omega$ and $R_2 = 3 k\Omega$ are connected in series across a constant supply of $10 V$. A real (non-ideal) voltmeter is used to measure the voltage across $R_2$. On its $6 V$ range, the meter reads $5 V$.