Ohm's Law

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 $10 \ \Omega$.

Each dry cell has an EMF of $1.5 \ \text{V}$ and the maximum current it can safely supply is $0.05 \ \text{A}$.

In the circuit shown, $R_1$, $R_2$, and $R_3$ are connected in series across the supply $U$. $R_2$ is a rheostat with slider $P$. Point $a$ is taken at the slider $P$, and point $b$ is at the node between $R_3$ and the negative terminal of the supply. Given $R_1 = 350\ \Omega$, $R_2 = 270\ \Omega$, $R_3 = 550\ \Omega$, and $U = 12$ V.

A circuit requires a resistor of resistance $15$ k$\Omega$, but only several $10$ k$\Omega$ resistors are available.

Three identical resistors are first connected in series to a power source, then connected in parallel to the same power source. The internal resistance of the power source is negligible. For the two connection methods, find the ratios (series to parallel) of:

A small light bulb has rated voltage $U_0 = 6$ V and rated power $P_0 = 18$ W. It is powered by a source with EMF $\varepsilon = 12$ V and internal resistance $r = 0.5\ \Omega$.

Six identical resistors, each of resistance $R$, are connected in the circuit shown in Figure. The battery has EMF $U$ and negligible internal resistance, and the resistance values do not change.

To measure the voltage between two points $A$ and $B$ in a circuit, a voltmeter is connected in parallel across those two points, as shown in Figure. The circuit consists of a battery with resistors $R_1$ and $R_2$ in series, and the voltmeter is placed across $R_2$ (between $A$ and $B$). The voltmeter's internal resistance $R_V$ is finite (not infinite).

To measure the current in a circuit, the circuit must be broken and an ammeter inserted in series, as shown. The circuit consists of a battery (emf $\varepsilon$, negligible internal resistance) connected to two resistors $R_1$ and $R_2$ in series. The ammeter has non-zero internal resistance $R_A$.

A voltmeter with a full-scale range of 150 V has an internal resistance of $R_V = 20$ kΩ. It is connected in series with an unknown high resistance $R$, and this combination is connected across a 110 V supply. The voltmeter reads 5 V.