27. Resistors & DC Circuits

A potentiometer is a device to precisely measure potential differences or emf, using a “null” technique. In the simple potentiometer circuit shown in Fig. 26–83, R′ represents the total resistance of the resistor from A to B (which could be a long uniform “slide” wire), whereas R represents the resistance of only the part from A to the movable contact at C. When the unknown emf to be measured, $E_x$, is placed into the circuit as shown, the movable contact C is moved until the galvanometer G gives a null reading (i.e., zero) when the switch S is closed. The resistance between A and C for this situation we call R_x. Next, a standard emf, $E_s$, which is known precisely, is inserted into the circuit in place of $E_x$ and again the contact C is moved until zero current flows through the galvanometer when the switch S is closed. The resistance between A and C now is called R_s. Show that the unknown emf is given by $E_x=\left(\frac{R_x}{R_s}\right)E_s$ where R_x, R_s and $E_s$ are all precisely known. The working battery (at top of circuit diagram), as well as the standard cell $E_s$, are assumed to be fresh and to give a constant voltage.

In the circuit shown in Fig. E26.34, the 6.0 Ω resistor is consuming energy at a rate of 24 J/s when the current through it flows as shown. What are the polarity and emf ε of the unknown battery, assuming it has negligible internal resistance?

A lightbulb is in series with a 2.0 Ω resistor. The lightbulb dissipates 10 W when this series circuit is connected to a 9.0 V battery. What is the current through the lightbulb? There are two possible answers; give both of them.

The circuit shown in Fig. E$25.33$ contains two batteries, each with an emf and an internal resistance, and two resistors. Find the current in the circuit (magnitude and direction).

The 5.00 V battery in Fig. E26.28 is removed from the circuit and replaced by a 15.00 V battery, with its negative terminal next to point b. The rest of the circuit is as shown in the figure. Find the current in each branch.

Draw a graph of the potential as a function of the distance traveled through the circuit, traveling cw from V = 0 V at the lower left corner.

The circuit shown in Fig. E$25.33$ contains two batteries, each with an emf and an internal resistance, and two resistors. Find the terminal voltage $V_{ab}$ of the $16.0$-V battery.

For the circuit below, calculate

(a) the voltage V₁ shown, and

(b) the current through the 6-Ohm resistor.

According to Kirchhoff's Loop Rule (Kirchhoff's Voltage Law), the algebraic sum of the potential differences (voltages) around any closed loop in a circuit is equal to what value?

The batteries shown in the circuit in Fig. E26.24 have negligibly small internal resistances. Find the current through the 30.0-Ω resistor.

In FIGURE EX28.30, what is the value of the potential at points 1 and 2?

What is the current through the 10 Ω resistor in FIGURE P28.61? Is the current from left to right or right to left?

The circuit shown in Fig. E$25.30$ contains two batteries, each with an emf and an internal resistance, and two resistors. Find the potential difference $V_{ac}$ of point $a$ with respect to point $c$.

For the circuit below, calculate the voltage across the 100-Ohm resistor.