A heart pacemaker is designed to operate at 72 beats/min using a 7.5-$\mu$F capacitor in a simple RC circuit. What value of resistance should be used if the pacemaker is to fire when the voltage reaches $63$ percent of maximum?

A three-way lightbulb can produce 50 W, 100 W, or 150 W, at 120 V. Such a bulb contains two filaments that can be connected to the 120 V individually or in parallel. Describe how the connections to the two filaments are made to give each of the three wattages. What must be the resistance of each filament?

Suppose that you wish to apply a 0.25-V potential difference between two points on the body. The resistance is about 2000 $\Omega$, and you only have a $9.0$-$\mathrm{V}$ battery. How can you connect up one or more resistors so that you can produce the desired voltage?

A 12.0-V battery (assume the internal resistance = 0) is connected to two resistors in series. A voltmeter whose internal resistance is 15.0 k$\Omega$ measures $5.5 ~\mathrm{V}$ and $4.0 ~\mathrm{V}$, respectively, when connected across each of the resistors. What is the resistance of each resistor?

The voltage across a 120-k$\Omega$ resistor in a circuit containing additional resistance $(R_2)$ in series with a battery (V) is measured, by a $20,000$-$\Omega/\mathrm{V}$ meter on the $100$-$\mathrm{V}$ scale, to be $25 ~\mathrm{V}$. On the $30$-$\mathrm{V}$ scale, the reading is $23 ~\mathrm{V}$. What is the actual voltage in the absence of the voltmeter? What is $R_2?$

What internal resistance should the voltmeter have to be in error by less than 3 percent for the situation of earlier Example?

Two 7.4-k$\Omega$ resistors are placed in series and connected to a battery. A voltmeter of sensitivity $1000 ~\Omega/\mathrm{V}$ is on the $3.0$-$\mathrm{V}$ scale and reads $2.0 ~\mathrm{V}$ when placed across either of the resistors. What is the emf of the battery? (Ignore its internal resistance.)

A battery with $\mathscr{E}$=12.0 V and internal resistance r=1.0 $\Omega$ is connected to two 9.0-k$\Omega$ resistors in series. An ammeter of internal resistance 0.50 $\Omega$ measures the current and at the same time a voltmeter with internal resistance 15 k$\Omega$ measures the voltage across one of the $9.0$-$\mathrm{k} \Omega$ resistors in the circuit. What do the ammeter and voltmeter read?

An ammeter whose internal resistance is 60 $\Omega$ reads 5.25 mA when connected in a circuit containing a battery and two resistors in series whose values are $700 ~\Omega$ and $400 ~\Omega$. What is the actual current when the ammeter is absent?

A 45-V battery of negligible internal resistance is connected to a 37-k$\Omega$ and a 28-k$\Omega$ resistor in series. What reading will a voltmeter, of internal resistance 100 k$\Omega$, give when used to measure the voltage across each resistor? What is the percent inaccuracy due to meter resistance for each case?

Three 240-$\Omega$ resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways and what is the net resistance in each case?

Household outlets are often double outlets. Are these connected in series or parallel? How do you know?

A milliammeter reads 10 mA full scale. It consists of a 0.20-$\Omega$ resistor in parallel with a 30-$\Omega$ galvanometer. How can you change this ammeter to a voltmeter giving a full-scale reading of $10 ~\mathrm{V}$ without taking the ammeter apart? What will be the sensitivity $(\Omega/\mathrm{V})$ of your voltmeter?

A galvanometer has a sensitivity of 35 k$\Omega/\mathrm{V}$ and internal resistance 20.0 $\Omega$. How could you make this into (a) an ammeter that reads $2.0 ~\mathrm{A}$ full scale, or (b) a voltmeter reading $1.00 ~\mathrm{V}$ full scale?