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 $R_2?$

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?

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

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?

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?

A galvanometer has an internal resistance of 30 $\Omega$ and deflects full scale for a 50-$\mu$A current. Describe how to use this galvanometer to make (a) an ammeter to read currents up to $30 ~\mathrm{A}$, and (b) a voltmeter to give a full-scale deflection of $1000 ~\mathrm{V}$.

An ammeter has a sensitivity of 10,000 $\Omega/\mathrm{V}$. What current passing through the galvanometer produces full-scale deflection?

What is the resistance of a voltmeter on the 250-V scale if the meter sensitivity is 30,000 $\Omega/\mathrm{V}?$

The RC circuit of earlier Fig. has R = 6.7 k$\Omega$ and C = 3.0 $\mu$F. The capacitor is at voltage $V_o$ at t = 0, when the switch is closed. How long does it take the capacitor to discharge to $1.0$ percent of its initial voltage?

In earlier figure, the total resistance is 15 k$\Omega$ and the battery's emf is 24.0 V. If the time constant is measured to be 35 $\mu$s, calculate (a) the total capacitance of the circuit and (b) the time it takes for the voltage across the resistor to reach $16.0 ~\mathrm{V}$.

Suppose a 7.5-$\mu$F capacitor replaced the 10.0-$\Omega$ resistor in earlier Figure. Calculate: (a) the charge on the capacitor in the steady state-that is, after the capacitor reaches its maximum charge; (b) the steady state current through the other resistors.

Describe carefully the difference between emf and potential difference.