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In Fig. 25-28, find the equivalent capacitance of the combination. Assume that ${\mathbf{C}}_{\mathbf{1}}\mathbf{is}\mathbf{}\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{μ¹ó}\mathbf{,}\mathbf{}{\mathbf{C}}_{\mathbf{2}}\mathbf{}\mathbf{is}\mathbf{}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{μ¹ó}\mathbf{,}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{C}}_{\mathbf{3}}\mathbf{}\mathbf{is}\mathbf{}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{}{\mathbf{μ¹ó}}_{\mathbf{}}$

When a dielectric slab is inserted between the plates of one of the two identical capacitors in Fig. 25-23, do the following properties of that capacitor increase, decrease, or remain the same: (a) capacitance, (b) charge, (c) potential difference, and (d) potential energy? (e) How about the same properties of the other capacitor?

In Fig. 25-29, find the equivalent capacitance of the combination. Assume that ${\mathbf{C}}_{\mathbf{1}}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{μ¹ó}$, ${\mathbf{C}}_{\mathbf{2}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{μ¹ó}$and${\mathbf{C}}_{\mathbf{3}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{μ¹ó}$

You are to connect capacitances ${\mathit{C}}_{\mathbf{1}}$and${\mathit{C}}_{\mathbf{2}}$, with${\mathit{C}}_{\mathbf{1}}\mathbf{>}{\mathit{C}}_{\mathbf{2}}$, to a battery, first individually, then in series, and then in parallel. Rank those arrangements according to the amount of charge stored, greatest first.

Two parallel-plate capacitors, 6.0$\mathbf{μ¹ó}$each, are connected in parallel to a 10 Vbattery. One of the capacitors is then squeezed so that its plate separation is 50.0% of its initial value. Because of the squeezing, (a) How much additional charge is transferred to the capacitors by the battery? (b) What is the increase in the total charge stored on the capacitors?

A 100 pFcapacitor is charged to a potential difference of 50 V,and the charging battery is disconnected. The capacitor is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first capacitor drops to 35 Vwhat is the capacitance of this second capacitor?

In Fig. 25-30, the battery has a potential difference of V = 10.0 V, and the five capacitors each have a capacitance of$\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{μ¹ó}$What is the charge on (a) capacitor 1 and (b) capacitor 2?

In Fig. 25-31, a 20.0 Vbattery is connected across capacitors of capacitances${\mathbf{C}}_{\mathbf{1}}\mathbf{=}{\mathbf{C}}_{\mathbf{6}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{μ¹ó}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{C}}_{\mathbf{3}}\mathbf{=}{\mathbf{C}}_{\mathbf{5}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}{\mathbf{C}}_{\mathbf{2}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}{\mathbf{C}}_{\mathbf{4}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{μ¹ó}$What are (a) the equivalent capacitance${\mathbf{C}}_{\mathbf{eq}}$of the capacitors and (b) the charge stored by${\mathbf{C}}_{\mathbf{eq}}$? What are (c)${\mathbf{V}}_{\mathbf{1}}$and (d)role="math" localid="1661748621904" ${\mathbf{q}}_1$of capacitor 1, (e)role="math" localid="1661748675055" ${\mathbf{V}}_{\mathbf{2}}$and (f)${\mathbf{q}}_{\mathbf{2}}$of capacitor 2, and (g)${\mathbf{V}}_{\mathbf{3}}$and (h)${\mathbf{q}}_{\mathbf{3}}$of capacitor 3?

Plot 1 in Fig. 25-32agives the charge qthat can be stored on capacitor 1 versus the electric potential Vset up across it. The vertical scale is set by${\mathit{q}}_{\mathbf{s}}\mathbf{=}\mathbf{16}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{μ°ä}$and the horizontal scale is set by${\mathbf{\text{V}}}_{\mathbf{s}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{V}$Plots 2 and 3 are similar plots for capacitors 2 and 3, respectively. Figure bshows a circuit with those three capacitors and abattery. What is the charge stored on capacitor 2 in that circuit?

In Fig. 25-29, a potential difference of V= 100.0 V is applied across a capacitor arrangement with capacitances,${\mathbf{C}}_{\mathbf{1}}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{μ¹ó}$,${\mathbf{C}}_{\mathbf{2}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{μ¹ó}$, and${\mathbf{C}}_3\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{μ¹ó}$.If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, (a) What is the increase in the charge on capacitor 1? (b) What is the increase in the potential difference across capacitor 1?