21.1 Resistors in Series and Parallel

Can any arbitrary combination of resistors be broken down into series and parallel combinations? See if you can draw a circuit diagram of resistors that cannot be broken down into combinations of series and parallel.

If the circuit in the previous question is modified by removing some of the 1.6 kΩ resistors, the total current in the circuit is 24 mA. How many resistors were removed?

1. 1
2. 2
3. 3
4. 4

In a circuit, a parallel combination of two 20-Ω and one 10-Ω resistors is connected in series with a 4-Ω resistor. The source voltage is 36 V.

1. Find the resistor(s) with the maximum current.
2. Find the resistor(s) with the maximum voltage drop.
3. Find the power dissipated in each resistor and hence the total power dissipated in all the resistors. Also find the power output of the source. Are they equ…

Note: Data taken from figures can be assumed to be accurate to three significant digits.

(a) What is the resistance of ten $\text{275}-\Omega$ resistors connected in series? (b) In parallel?

Note: Data taken from figures can be assumed to be accurate to three significant digits.

What are the largest and smallest resistances you can obtain by connecting a $\text{36} . 0-Ω$, a $\text{50} . 0-Ω$, and a $\text{700}-\Omega$ resistor together?

Note: Data taken from figures can be assumed to be accurate to three significant digits.

Your car’s 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.0-V system. What power would one headlight and the starter consume if connected in series to a 12.0-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)

Note: Data taken from figures can be assumed to be accurate to three significant digits.

Referring to the example combining series and parallel circuits and the figure, calculate $I_{3}$ in the following two different ways: (a) from the known values of $I$ and $I_{2}$; (b) using Ohm’s law for $R_{3}$. In both parts explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Res…

Note: Data taken from figures can be assumed to be accurate to three significant digits.

Refer to the figure and the discussion of lights dimming when a heavy appliance comes on. (a) Given the voltage source is 120 V, the wire resistance is $0 . \text{400} \Omega$, and the bulb is nominally 75.0 W, what power will the bulb dissipate if a total of 15.0 A passes through the wires when the motor comes on? Assume negligib…

Note: Data taken from figures can be assumed to be accurate to three significant digits.

Show that if two resistors $R_{1}$ and $R_{2}$ are combined and one is much greater than the other ($R_{1} >> R_{2}$): (a) Their series resistance is very nearly equal to the greater resistance $R_{1}$. (b) Their parallel resistance is very nearly equal to smaller resistance $R_{2}$.

Note: Data taken from figures can be assumed to be accurate to three significant digits.

Two resistors, one having a resistance of $9 \text{00 k}\Omega$, are connected in series to produce a total resistance of $0 . \text{500 M}\Omega$. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?