Figure $a$ and $b$ displays two circuits with a charged capacitor that is to be discharged through a resistor when the switch is closed. In Fig. $a$, $R_1=20.0 \mathrm{\Omega }$, $C_1=5.00 \mathrm{\mu F}.$In Fig.$b$, $R_2=10.0 \mathrm{\Omega }$ and $C_2=8.00 \mathrm{\mu F}$. The ratio of the initial charges on the two capacitors is $\frac{q_{02}}{q_{{01}_{}}}=1.75$. At time $t=0$ both switches are closed. At what time do the two capacitors have the same charge?

In fig., circuit section $AB$ absorbs energy at a rate of $50 \mathrm{W}$ when current $i=2.0 \mathrm{A}$ passes through it in the indicated direction. Resistance $\mathrm{R}=2.0 \mathrm{\Omega }.$

$\left(a\right)$ What is the potential difference between $A$ and $B ?$ Emf device $X$ lacks internal resistance.

$\left(b\right)$ What is its emf?

$\left(c\right)$ Is point $B$ connected to the positive terminal of $X$ or to the negative terminal?

In fig., $a,$ both batteries have emf $\mathcal{E}=1.20 \mathrm{V}$ and the external resistance $R$ is a variable resistor. Fig., $b$, gives the electric potential $V$ between the terminals of each battery as functions of $R:$ Curve $1$ corresponds to battery and curve $2$ corresponds to battery $2$. The horizontal scale is set by $R_s=0.40 \Omega .$ What is the internal resistance of $\left(a\right)$ battery $1$ and $\left(b\right)$ battery $2 ?$

(a)                                                                  (b)

In figure, the resistances are $R_1=1.0 \mathrm{\Omega }$ and $R_2=2.0 \mathrm{\Omega }$ and the ideal batteries have emfs ${\epsilon }_1=2.0 \mathrm{V}$ and ${\epsilon }_2={\epsilon }_3=4.0 \mathrm{V}.$ What are the $\left(a\right)$ size, $\left(b\right)$ direction (up or down) of the current in battery $1$ and the $\left(c\right)$ size, $\left(d\right)$ direction of the current in battery $2 ?$ $\left(e\right)$ Is battery $1$ absorbing or providing energy and $\left(f\right)$ at what rate? $\left(g\right)$ What is the potential difference $V_a-V_b ?$

In the following figure, a voltmeter of resistance $R_{\mathrm{V}}=300 \mathrm{\Omega }$ and an ammeter of resistance $R_{\mathrm{A}}=3.00 \mathrm{\Omega }$ are being used to measure a resistance $R$ in a circuit that also contains a resistance $R_0=100 \mathrm{\Omega }$ and an ideal battery of emf $\epsilon =28.5 \mathrm{V}$. Resistance $R$ is given by $R=V/i$, where $V$ is the voltmeter reading and $i$ is the current in resistance $R$. However, the ammeter reading is not $i$ but rather $i^{\text{'}},$ which is $i$ plus the current through the voltmeter. Thus, the ratio of the two meter readings is not $R$ but only an apparent resistance $R^{\text{'}}=V/i^{\text{'}}$. If $R=85.0 \mathrm{\Omega }$, what are (a) the ammeter reading, (b) the voltmeter reading, and (c) $R^{\text{'}}$? (d) If $R_{\mathrm{V}}$ is increased, does the difference between $R^{\text{'}}$ and $R$ increase, decrease, or remain the same?

A $3.00 \mathrm{M\Omega }$ resistor and a $1.00 \mu \mathrm{F}$ capacitor are connected in series with an ideal battery of emf $\epsilon =4.00 \mathrm{V}$ . At $6.00 \mathrm{s}$ after the connection is made, what is the rate at which

(a) the charge of the capacitor is increasing? 

(b) energy is being stored in the capacitor? 

(c) thermal energy is appearing in the resistor?

(d) energy is being delivered by the battery?