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黿¥µæ¿é¢ç©ãšé»æ¥µæ¿ééãå
±ã« $S[m^2]$ ãš $d[m]$ ã§,äžæ¹ã¯æ¯èªé»çã $\epsilon_{r1}$ ã®èªé»äœãããªãå¹³è¡å¹³æ¿ã³ã³ãã³ãµ $C_1$ ãšã仿¹ã¯æ¯èªé»çã $\epsilon_{r2}$ ã®èªé»äœãããªãå¹³è¡å¹³æ¿ã³ã³ãã³ãµ $C_2$ ããããä»ãããããå³ã®ããã«äžŠåã«æ¥ç¶ã 端å A, Béã«çŽæµé»å§ $V_0$ [V]ãå ããããã®ãšã,ã³ã³ãã³ãµ $C_1$ ã®é»æ¥µæ¿éã®é»çã®åŒ·ãã $E_1[V/m]$,黿å¯åºŠã $D_1[C/m^2]$,ãŸã,ã³ã³ãã³ãµ $C_2$ ã®é»æ¥µæ¿éã®é»çã®åŒ·ãã $E_2[V/m]$,黿å¯åºŠã $D_2[C/m^2]$ ãšãããäž¡ã³ã³ãã³ãµã®é»çã®åŒ·ã $E_1[V/m]$ ãš $E_2$ [V/m] ã¯ãããã (ã¢) ã§ããã黿å¯åºŠ $D_1[C/m^2]$ ãš $D_2[C/m^2]$ ã¯ãããã (ã€) ã§ããããããã£ãŠ,ã³ã³ãã³ãµ $C_1$ ã«èããããé»è·ã $Q_1$ [C], ã³ã³ãã³ãµ $C_2$ ã«èããããé»è·ã $Q_2$ [C] ãšãããšããããã¯ãããã (ãŠ) ãšãªãã
ãã ãã黿¥µæ¿ã®åãåã³ã³ã³ãã³ãµã®ç«¯å¹æã¯ãç¡èŠã§ãããã®ãšããããŸããç空ã®èªé»çã $\epsilon_0[F/m]$ ãšããã
äžèšã®èšè¿°äžã®ç©ºçœç®æ(ã¢)~(ãŠ)ã«åœãŠã¯ãŸãåŒã®çµåããšããŠãæ£ãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
| – | (ã¢) | (ã€) | (ãŠ) |
|---|---|---|---|
| (1) | $E_1=\frac{\epsilon_{r1}}{d}V_0$ã $E_2=\frac{\epsilon_{r2}}{d}V_0$ | $D_1=\frac{\epsilon_{r1}}{d}SV_0$ã $D_2=\frac{\epsilon_{r2}}{d}SV_0$ | $Q_1=\frac{\epsilon_0\epsilon_{r1}}{d}SV_0$ã $Q_2=\frac{\epsilon_0\epsilon_{r2}}{d}SV_0$ |
| (2) | $E_1=\frac{\epsilon_{r1}}{d}V_0$ã $E_2=\frac{\epsilon_{r2}}{d}V_0$ | $D_1=\frac{\epsilon_0\epsilon_{r1}}{d}V_0$ã $D_2=\frac{\epsilon_0\epsilon_{r2}}{d}V_0$ | $Q_1=\frac{\epsilon_0\epsilon_{r1}}{d}SV_0$ã $Q_2=\frac{\epsilon_0\epsilon_{r2}}{d}SV_0$ |
| (3) | $E_1=\frac{V_0}{d}$ã $E_2=\frac{V_0}{d}$ | $D_1=\frac{\epsilon_0\epsilon_{r1}}{d}SV_0$ã $D_2=\frac{\epsilon_0\epsilon_{r2}}{d}SV_0$ | $Q_1=\frac{\epsilon_0\epsilon_{r1}}{d}V_0$ã $Q_2=\frac{\epsilon_0\epsilon_{r2}}{d}V_0$ |
| (4) | $E_1=\frac{V_0}{d}$ã $E_2=\frac{V_0}{d}$ | $D_1=\frac{\epsilon_0\epsilon_{r1}}{d}V_0$ã $D_2=\frac{\epsilon_0\epsilon_{r2}}{d}V_0$ | $Q_1=\frac{\epsilon_0\epsilon_{r1}}{d}SV_0$ã $Q_2=\frac{\epsilon_0\epsilon_{r2}}{d}SV_0$ |
| (5) | $E_1=\frac{\epsilon_0\epsilon_{r1}}{d}SV_0$ã $E_2=\frac{\epsilon_0\epsilon_{r2}}{d}SV_0$ | $D_1=\frac{\epsilon_0\epsilon_{r1}}{d}V_0$ã $D_2=\frac{\epsilon_0\epsilon_{r2}}{d}V_0$ | $Q_1=\frac{\epsilon_0}{d}SV_0$ã $Q_2=\frac{\epsilon_0}{d}SV_0$ |
解説
æ£è§£ã¯(4)ã§ãã
ã³ã³ãã³ãµ $C_1, C_2$ ã¯äžŠåæ¥ç¶ãããŠãããããã©ã¡ãã®ã³ã³ãã³ãµã«ãé»å§ $V_0$ ãããããŸãããããã£ãŠé»çã®åŒ·ãã¯æ¬¡åŒã®ããã«ãªããŸãã
$$E_1 = E_2 = \frac{V_0}{d}$$
黿å¯åºŠ $D$ 㯠$D = \epsilon E$ ã§ãããããããããæ¬¡åŒã®ããã«ãªããŸãã
$$D_1 = \epsilon_0\epsilon_{r1}E_1 = \frac{\epsilon_0\epsilon_{r1}}{d}V_0$$
$$D_2 = \epsilon_0\epsilon_{r2}E_2 = \frac{\epsilon_0\epsilon_{r2}}{d}V_0$$
ã³ã³ãã³ãµã«èããããé»è· $Q$ 㯠$Q = DS$ ã§ãããããããããæ¬¡åŒã®ããã«ãªããŸãã
$$Q_1 = D_1S = \frac{\epsilon_0\epsilon_{r1}}{d}SV_0$$
$$Q_2 = D_2S = \frac{\epsilon_0\epsilon_{r2}}{d}SV_0$$
ã什å5å¹ŽåºŠäžæã»å2ãéé»çã«é¢ããæ§è³ª
éé»çã«é¢ããæ¬¡ã®èšè¿°ã®ãã¡ã誀ã£ãŠãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) åªè³ªäžã«çœ®ãããæ£é»è·ããåºã黿°åç·ã®æ¬æ°ã¯ããã®é»è·ã®å€§ããã«æ¯äŸã,åªè³ªã®èªé»çã«åæ¯äŸããã
(2) é»çäžã«ããã黿°åç·ã¯ãçžäºã«äº€å·®ããªãã
(3) é»çäžã«ããã黿°åç·ã¯ãçé»äœé¢ãšçŽäº€ããã
(4) é»çäžã®ããç¹ã®é»æ°åç·ã®å¯åºŠã¯ããã®ç¹ã«ãããé»çã®åŒ·ã(倧ãã)ã衚ãã
(5) é»çäžã«çœ®ãããå°äœå
éšã®é»çã®åŒ·ã(倧ãã)ã¯ããã®å°äœè¡šé¢ã®é»çã®åŒ·ã(倧ãã)ã«çããã
解説
æ£è§£ã¯(5)ã§ãã
éé»å¹³è¡¡ç¶æ ã«ããå°äœã®å éšã§ã¯ãé»è·ã®ç§»åãèµ·ããŠããªããããå°äœå éšã®é»çã®åŒ·ãã¯åžžã«é¶ãšãªããŸãããããã£ãŠãå°äœè¡šé¢ã®é»çã®åŒ·ããšçãããšãã(5)ã®èšè¿°ã誀ããšãªããŸãã
ã什å5å¹ŽåºŠäžæã»å3ãç£æ°åè·¯ã®ç£æ°æµæ
ç£æ°åè·¯ã«ãããç£æ°æµæã«é¢ããæ¬¡ã®èšè¿°ã®ãã¡ã誀ã£ãŠãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) ç£æ°æµæã¯ã次ã®åŒã§è¡šããããç£æ°æµæ=èµ·ç£å/ç£æ
(2) ç£æ°æµæã¯ãç£è·¯ã®æé¢ç©ã«æ¯äŸããã
(3) ç£æ°æµæã¯ãæ¯éç£çã«åæ¯äŸããã
(4) ç£æ°æµæã¯ãç£è·¯ã®é·ãã«æ¯äŸããã
(5) ç£æ°æµæã®åäœã¯ã $[H^{-1}]$ ã§ããã
解説
æ£è§£ã¯(2)ã§ãã
ç£æ°æµæ $R_m$ ã¯ãç£è·¯ã®é·ãã $l$ãæé¢ç©ã $S$ãéç£çã $\mu$ ãšãããšæ¬¡åŒã§è¡šãããŸãã
$$R_m = \frac{l}{\mu S}$$
ãã®åŒãããç£æ°æµæã¯ç£è·¯ã®æé¢ç© $S$ ã«åæ¯äŸããããšãããããŸãããããã£ãŠ(2)ã誀ããšãªããŸãã
ã什å5å¹ŽåºŠäžæã»å4ãç£çåã³ç£æã«é¢ããæ§è³ª
ç£çåã³ç£æã«é¢ããèšè¿°ãšããŠã誀ã£ãŠãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 1måœããã®å·»æ°ãNã®ç¡éã«é·ããœã¬ãã€ãã«é»æµI [A] ãæµããšããœã¬ãã€ãã®å
éšã«ã¯ç£ç H = NI [A/m] ãçãããç£çã®å€§ããã¯ããœã¬ãã€ãã®å¯žæ³ãå
éšã«ååšããç©è³ªã®çš®é¡ã«åœ±é¿ãããªãã
(2) åäžç£çäžã«ãããŠãç£çã®æ¹åãšçŽè§ã«çœ®ãããçŽç·ç¶å°äœã«çŽæµé»æµãæµããšãå°äœã«ã¯é»æµã®å€§ããã«æ¯äŸããåãåãã
(3) 2æ¬ã®å¹³è¡ãªçŽç·ç¶å°äœã«å察åãã®é»æµãæµããšãå°äœã«ã¯å°äœéè·é¢ã®2ä¹ã«åæ¯äŸããåçºåãåãã
(4) ãã¬ãã³ã°ã®å·Šæã®æ³åã§ã¯ã芪æã®åããå°äœã«åãåã®åãã瀺ãã
(5) ç£æ°åè·¯ã«ãããŠãéç£çã¯é»æ°åè·¯ã®å°é»çã«ãç£æã¯é»æ°åè·¯ã®é»æµã«ãããã察å¿ããã
解説
æ£è§£ã¯(3)ã§ãã
2æ¬ã®å¹³è¡ãªçŽç·ç¶å°äœã«é»æµãæµãããšãã«åãå $F$ ã¯ã黿µã $I_1, I_2$ãè·é¢ã $r$ ãšãããšæ¬¡åŒã§è¡šãããŸãã
$$F = \frac{\mu_0 I_1 I_2}{2\pi r}$$
ãã®åŒãããå°äœã«åãåã¯è·é¢ $r$ ã«åæ¯äŸããããšãããããŸããè·é¢ã®2ä¹ã«åæ¯äŸããããã§ã¯ãªãããã(3)ã誀ããšãªããŸãã
ã什å5å¹ŽåºŠäžæã»å5ãçŽæµåè·¯ã®æ¶è²»é»å
å³ã®çŽæµåè·¯ã«ãããŠ,æµæ $R=10~\Omega$ ã§æ¶è²»ãããé»åã®å€ [W]ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.28 (2) 1.89 (3) 3.79 (4) 5.36 (5) 7.62
解説
æ£è§£ã¯(1)ã§ãã
ãããã³ã®å®çãçšããŠãæµæ $R=10~\Omega$ ã«æµãã黿µãæ±ããŸããåè·¯ã $R$ ã®éšåã§åãé¢ããéæŸé»å§ $V_0$ ãšåææµæ $R_0$ ãèšç®ããããšã§ãæ¶è²»ãããé»åãå°åºããããšãã§ããŸãã
ã什å5å¹ŽåºŠäžæã»å6ãçŽæµåè·¯ã®é»æµ
å³ã®ãããªçŽæµåè·¯ã«ãããŠã3Î©ã®æµæãæµãã黿µã®å€[A]ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.35 (2) 0.45 (3) 0.55 (4) 0.65 (5) 0.75
解説
æ£è§£ã¯(5)ã§ãã
ãã«ããããã®æ³åãéãåããã®çãªã©ãé©çšããéåè·¯ããšã«æ¹çšåŒãç«ãŠãããšã§åæµæã«æµãã黿µãæ±ããããšãã§ããŸãã
ã什å5å¹ŽåºŠäžæã»å7ãæµæã®æž©åºŠå€åãšé»æµ
å³ã®åè·¯ã«ãããŠãã¹ã€ããSãéããçŽæµé»æºããéå±è£œã®æµæã«é»æµãæµãããšããçºç±ã«ããæµæã®æž©åºŠã120âã«ãªã£ããã¹ã€ããSãéããçŽåŸã«åè·¯ãæµãã黿µã«æ¯ã¹ãæµæã®æž©åºŠã120âã«ãªã£ããšãã«åè·¯ãæµãã黿µã¯ãã©ã®ããã«å€åããããæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
ãã ããã¹ã€ããSãéããçŽåŸã®æµæã®æž©åºŠã¯20âãšããæµæã®æž©åºŠä¿æ°ã¯äžå®ã§ 0.005 â-1ãšããããŸããçŽæµé»æºã®èµ·é»åã®å€§ããã¯æž©åºŠã«ãããäžå®ãšããçŽæµé»æºã®å
éšæµæã¯ç¡èŠã§ãããã®ãšããã
(1) å€åããªã (2) 50%å¢å (3) 33%æžå° (4) 50%æžå° (5) 33%å¢å
解説
æ£è§£ã¯(3)ã§ãã
枩床 $t$ ã«ãããæµæ $R_t$ ã¯ãåºæºæž©åºŠã20âãšããå Žåãæ¬¡åŒã§è¡šãããŸãã
$$R_{120} = R_{20} {1 + 0.005(120 – 20)} = R_{20} (1 + 0.5) = 1.5 R_{20}$$
æµæå€ã1.5åã«ãªã£ãããããªãŒã ã®æ³åã«ãã黿µã¯ $\frac{1}{1.5} \approx 0.67$ åãšãªããŸããã€ãŸããå ã®é»æµããçŽ33%æžå°ããããšã«ãªããŸãã
ã什å5å¹ŽåºŠäžæã»å8ãRLCçŽåå ±æ¯åè·¯
æ¬¡ã®æç« ã¯ãRLC çŽåå
±æ¯åè·¯ã«é¢ããèšè¿°ã§ããã
R [ ]ã®æµæãã€ã³ãã¯ã¿ã³ã¹L [H]ã®ã³ã€ã«ãéé»å®¹éC [F]ã®ã³ã³ãã³ãµãçŽåã«æ¥ç¶ããåè·¯ãããã
ãã®åè·¯ã«äº€æµé»å§ãå ã,ãã®åšæ³¢æ°ãå€åããããšãç¹å®ã®åšæ³¢æ° $f_r$ [Hz]ã®ãšãã«èªå°æ§ãªã¢ã¯ã¿ã³ã¹ $X_L = 2\pi f_r L$ [Ω]ãšå®¹éæ§ãªã¢ã¯ã¿ã³ã¹ $X_C = \frac{1}{2\pi f_r C}$ [Ω]ã®å€§ãããçãããªãããã®äœçšãäºãã«æã¡æ¶ãåã£ãŠåè·¯ã®ã€ã³ããŒãã³ã¹ã (ã¢) ãªãã (ã€) 黿µãæµããããã«ãªãããã®çŸè±¡ãçŽåå
±æ¯ãšãã,ãã®ãšãã®åšæ³¢æ° $f_r$ [Hz] ããã®åè·¯ã®å
±æ¯åšæ³¢æ°ãšãããåè·¯ã®ãªã¢ã¯ã¿ã³ã¹ã¯å
±æ¯åšæ³¢æ° $f_r$ [Hz]ããäœãåšæ³¢æ°ã§ã¯ (ãŠ) ãšãªããé»å§ããäœçžã (ãš) 黿µãæµããããŸã,å
±æ¯åšæ³¢æ° $f_r$ [Hz]ããé«ãåšæ³¢æ°ã§ã¯ (ãª) ãšãªããé»å§ããäœçžã (ã«) 黿µãæµããã
äžèšã®èšè¿°äžã®ç©ºçœç®æ(ã¢)~(ã«)ã«åœãŠã¯ãŸãçµåããšããŠãæ£ãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
| – | (ã¢) | (ã€) | (ãŠ)ã»(ãš)ã»(ãª)ã»(ã«) |
|---|---|---|---|
| (1) | 倧ãã | å°ã㪠| é ããã»èªå°æ§ã»å®¹éæ§ã»é²ãã |
| (2) | å°ãã | 倧ã㪠| é²ãã ã»å®¹éæ§ã»é ããã»èªå°æ§ |
| (3) | å°ãã | 倧ã㪠| 容鿧ã»é²ãã ã»èªå°æ§ã»é ãã |
| (4) | 倧ãã | å°ã㪠| èªå°æ§ã»é ããã»é²ãã ã»å®¹éæ§ |
| (5) | å°ãã | 倧ã㪠| 容鿧ã»é ããã»èªå°æ§ã»é²ãã |
解説
æ£è§£ã¯(3)ã§ãã
çŽåå
±æ¯æããªã¢ã¯ã¿ã³ã¹ãæã¡æ¶ãåãããåè·¯ã®ã€ã³ããŒãã³ã¹ã¯æå°ãšãªããæå€§ã®é»æµãæµããŸãã
åšæ³¢æ°ãå
±æ¯åšæ³¢æ°ããäœãå Žåã¯å®¹éæ§ãªã¢ã¯ã¿ã³ã¹ã®åœ±é¿ã倧ãããªããããåè·¯ã¯å®¹éæ§ãšãªããé»å§ãã黿µã®äœçžãé²ã¿ãŸãã
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±æ¯åšæ³¢æ°ããé«ãå Žåã¯èªå°æ§ãªã¢ã¯ã¿ã³ã¹ã®åœ±é¿ã倧ãããªããããåè·¯ã¯èªå°æ§ãšãªããé»å§ãã黿µã®äœçžãé
ããŸãã
ã什å5å¹ŽåºŠäžæã»å9ã亀æµåè·¯ã®åç
å³ã®ããã«ãæµæR [ ]ãšèªå°æ§ãªã¢ã¯ã¿ã³ã¹ $X_L$ [Q]ãçŽåã«æ¥ç¶ããã亀æµåè·¯ãããã $\frac{R}{X_L}=\frac{1}{\sqrt{2}}$ ã®é¢ä¿ããããšã,ãã®åè·¯ã®åç $\cos\theta$ ã®å€ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.43 (2) 0.50 (3) 0.58 (4) 0.71 (5) 0.87
解説
æ£è§£ã¯(3)ã§ãã
RLçŽååè·¯ã®åç $\cos\theta$ ã¯æ¬¡åŒã§æ±ããããŸãã
$$\cos\theta = \frac{R}{\sqrt{R^2 + X_L^2}} = \frac{1}{\sqrt{1 + (\frac{X_L}{R})^2}}$$
æ¡ä»¶ãã $\frac{X_L}{R} = \sqrt{2}$ ã§ãããããä»£å ¥ããŠèšç®ããŸãã
$$\cos\theta = \frac{1}{\sqrt{1 + (\sqrt{2})^2}} = \frac{1}{\sqrt{3}} \approx 0.58$$
ã什å5å¹ŽåºŠäžæã»å10ãã€ã³ãã¯ã¿ã³ã¹ã«çããé»å§
å³1ã®ããã«ãã€ã³ãã¯ã¿ã³ã¹L=5Hã®ã³ã€ã«ã«çŽæµé»æµæº ã黿µi [mA]ãäŸçµŠããŠããåè·¯ãããã黿µi [mA] ã¯å³2ã®ãããªæéå€åãããŠããããã®ãšã,ã³ã€ã«ã®ç«¯åéã«çŸããé»å§ã®å€§ãã |v|ã®æå€§å€[V]ãšããŠ,æãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.25 (2) 0.5 (3) 1 (4) 1.25 (5) 1.5
解説
æ£è§£ã¯(4)ã§ãã
ã³ã€ã«ã®ç«¯åéã«çŸããé»å§ã®å€§ãã $|v|$ ã¯ã黿µã®æéå€åçãçšããŠæ¬¡åŒã§æ±ããããŸãã
$$|v| = L \left| \frac{\Delta i}{\Delta t} \right|$$
ã°ã©ããã黿µã®å€åç $\frac{\Delta i}{\Delta t}$ ãæå€§ãšãªãåºéãèŠã€ããŸããå€åçãæå€§ãšãªãåºéã«ãããŠèšç®ãããšãé»å§ã¯1.25VãšãªããŸãã
ã什å5å¹ŽåºŠäžæã»å11ãããŒã«çŽ åã®åäœåç
æ¬¡ã®æç« ã¯ãå³1åã³å³2ã«ç€ºãåçå³ãçšããŠããŒã«çŽ åã®åäœåçã«ã€ããŠè¿°ã¹ããã®ã§ããã
å³1ã«ç€ºãããã«ãp圢åå°äœã«çŽæµé»æµI [A]ãæµããåå°äœã®è¡šé¢ã«å¯ŸããŠåçŽã«äžããäžåãã«ç£æå¯åºŠB [T]ã®å¹³çç£çãåå°äœã«ããããšãåå°äœå
ã®æ£åã¯é²è·¯ãæ²ãããã黿¥µâ ã«ã¯ (ã¢) é»è·,黿¥µâ¡ã«ã¯ (ã€) é»è·ãååžããåå°äœã®å
éšã«é»çãçããããŸããå³2ã®n圢åå°äœã®å Žåã¯ãé»çã®æ¹åã¯p圢åå°äœã®æ¹åãš (ãŠ) ã§ããããã®é»çã«ããã黿¥µâ -â¡éã«ããŒã«é»å§ $V_H = R_H \times$ (ãš) [V]ãçºçããã
ãã ã,d [m]ã¯åå°äœã®åãã瀺ã, $R_H$ ã¯æ¯äŸå®æ° $[m^3/C]$ ã§ããã
äžèšã®èšè¿°äžã®ç©ºçœç®æ(ã¢)~(ãš)ã«åœãŠã¯ãŸãçµåããšããŠãæ£ãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
| – | (ã¢) | (ã€) | (ãŠ) | (ãš) |
|---|---|---|---|---|
| (1) | è² | æ£ | åã | $\frac{B}{Id}$ |
| (2) | è² | æ£ | åã | $\frac{Id}{B}$ |
| (3) | æ£ | è² | åã | $\frac{d}{BI}$ |
| (4) | è² | æ£ | å察 | $\frac{BI}{d}$ |
| (5) | æ£ | è² | å察 | $\frac{BI}{d}$ |
解説
æ£è§£ã¯(5)ã§ãã
p圢åå°äœã§ã¯å€æ°ãã£ãªã¢ã§ããæ£åïŒæ£é»è·ïŒã黿µãšåãåãã«ç§»åããããŒã¬ã³ãåã«ãã£ãŠé»æ¥µâ ã®æ¹åã«æ²ããããŸãããã®ãã黿¥µâ ã«æ£é»è·ã黿¥µâ¡ã«è² é»è·ãèç©ãããŸãã
n圢åå°äœã§ã¯å€æ°ãã£ãªã¢ã§ããé»åïŒè² é»è·ïŒã黿µãšéåãã«ç§»åããåæ§ã«ããŒã¬ã³ãåãåããŠé»æ¥µâ ã®æ¹åã«æ²ããããŸãããã®ãã黿¥µâ ã«è² é»è·ãèç©ãããé»çã®æ¹åã¯å察ã«ãªããŸãã
ããŒã«é»å§ $V_H$ ã¯æ¬¡åŒã§è¡šãããŸãã
$$V_H = R_H \frac{BI}{d}$$
ã什å5å¹ŽåºŠäžæã»å12ããŒãŒããã¯å¹æ
å³ã®ããã«ãç°ãªã2çš®é¡ã®éå±A, Bã§äžã€ã®éåè·¯ãäœãããã®äºã€ã®æ¥åç¹ãç°ãªã枩床ã«ä¿ãŠã°ã (ã¢)ããã®çŸè±¡ã (ã€) 广ãšããã
äžèšã®èšè¿°äžã®ç©ºçœç®æ(ã¢)åã³(ã€)ã«åœãŠã¯ãŸãçµåããšããŠãæ£ãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
| – | (ã¢) | (ã€) |
|---|---|---|
| (1) | 黿µãæµãã | ããŒã« |
| (2) | æµæãå€åãã | ããŒã« |
| (3) | éå±ã®é·ããå€åãã | ãŒãŒãã㯠|
| (4) | é»äœå·®ãçãã | ãã«ãã§ |
| (5) | èµ·é»åãçãã | ãŒãŒãã㯠|
解説
æ£è§£ã¯(5)ã§ãã
2çš®é¡ã®ç°ãªãéå±ã®äž¡ç«¯ãæ¥åããŠéåè·¯ãäœããäºã€ã®æ¥åéšã«æž©åºŠå·®ãäžãããšããã®åè·¯ã«èµ·é»åãçããŠé»æµãæµããŸãããã®çŸè±¡ããŒãŒããã¯å¹æãšãããŸãã
ã什å5å¹ŽåºŠäžæã»å13ãã³ã¬ã¯ã¿æ¥å°å¢å¹ åè·¯
å³ã®ã³ã¬ã¯ã¿æ¥å°å¢å¹ åè·¯ã«é¢ããèšè¿°ãšããŠã誀ã£ãŠãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) é»å§å¢å¹
床ã¯çŽ1ã§ããã
(2) å
¥åã€ã³ããŒãã³ã¹ã倧ããã
(3) åºåã€ã³ããŒãã³ã¹ãå°ããã
(4) ç·©è¡å¢å¹
åšãšããŠäœ¿çšãããããšãããã
(5) å¢å¹
åè·¯å
éšã§çºçããã²ãã¿ã倧ããã
解説
æ£è§£ã¯(5)ã§ãã
ã³ã¬ã¯ã¿æ¥å°å¢å¹ åè·¯ïŒãšããã¿ããã¯åè·¯ïŒã¯ãè² åž°éãæ·±ãããã£ãŠãããããå¢å¹ åè·¯å éšã§çºçããã²ãã¿ã¯å°ãããªããŸãããããã£ãŠ(5)ã誀ããšãªããŸãã
ã什å5å¹ŽåºŠäžæã»å14ãäºé»åèšæ³ã«ããäžçžé»åã®æž¬å®
å³ã®ããã«ãç·éé»å§200Vã®å¯Ÿç§°äžçžäº€æµé»æºããäžçžå¹³è¡¡è² è·ã«äŸçµŠããé»åãäºé»åèšæ³ã§æž¬å®ããã2å°ã®é»åèš $W_1$ åã³ $W_2$ ãæ£ããæ¥ç¶ãããšãããé»åèš $W_2$ ã®æéã鿝ããèµ·ããããé»åèš $W_2$ ã®é»å§ç«¯åã®æ¥µæ§ãå転ããŠæ¥ç¶ããåŸã2å°ã®é»åèšã®æç€ºå€ã¯ãé»åèš $W_1$ ã 490W,é»åèš $W_2$ ã 25 Wã§ãã£ãããã®ãšãã®å¯Ÿç§°äžçžäº€æµé»æºãäžçžå¹³è¡¡è² è·ã«äŸçµŠããé»åã®å€[W]ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
ãã ããäžçžäº€æµé»æºã®çžå転ã¯a, b, cã®é ãšããé»åèšã®é»åæå€±ã¯ç¡èŠã§ãããã®ãšããã
(1) 25 (2) 258 (3) 465 (4) 490 (5) 515
解説
æ£è§£ã¯(3)ã§ãã
äºé»åèšæ³ã§ã¯ãäžçžé»å $P$ ã¯2å°ã®é»åèšã®æç€ºå€ã®åãšããŠæ±ããããŸããäžæ¹ã®é»åèšã鿝ããèµ·ãããé»å§ç«¯åã®æ¥µæ§ãå転ãããŠæž¬å®ããå Žåããã®å€ã¯è² ã®å€ãšããŠèšç®ããå¿ èŠããããŸãã
$$P = W_1 + W_2 = 490 + (-25) = 465 \text{ [W]}$$
ã什å5å¹ŽåºŠäžæã»å15ã平衡äžçžåè·¯ã®æ¶è²»é»å
å³ã®å¹³è¡¡äžçžåè·¯ã«ã€ããŠã次ã®(a)åã³(b)ã®åã«çããã
(a) 端åa, cã«100Vã®åçžäº€æµé»æºãæ¥ç¶ãããšãããåè·¯ã®æ¶è²»é»åã¯200Wã§ãã£ããæµæRã®å€[ ]ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.30 (2) 30 (3) 33 (4) 50 (5) 83
(b) 端å a, b, c ã«ç·éé»å§ 200Vã®å¯Ÿç§°äžçžäº€æµé»æºãæ¥ç¶ãããšãã®å
šæ¶è²»é»åã®å€[kW]ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.48 (2) 0.80 (3) 1.2 (4) 1.6 (5) 4.0
解説
(a) æ£è§£ã¯(2)ã§ãã
端åa, céã«åçžäº€æµé»æºãæ¥ç¶ããå Žåãåè·¯ã®æ§æãè§£ãã»ãããŠç«¯åéã®åææµæ $R_{ac}$ ãæ±ããŸããæ¶è²»é»åãšé»å§ã®é¢ä¿ããåææµæãå°åºãããããã«æµæ $R$ ã®å€ãèšç®ããããšãã§ããŸãã
(b) æ£è§£ã¯(4)ã§ãã
äžçžé»æºãæ¥ç¶ãããšãã®åè·¯ã®1çžåã®ç䟡åè·¯ãèããYçµç·ã $\Delta$ çµç·ã®å€æãªã©ãçšããŠå
šæ¶è²»é»åãèšç®ããŸãã
ã什å5å¹ŽåºŠäžæã»å16ãçŽæµé»å§èšã䜿çšããæž¬å®
å
éšæµæã 15kΩã®150V 枬å®ç«¯åãšå
éšæµæã 10kΩã®100V 枬å®ç«¯åããã€æ°žä¹
ç£ç³å¯åã³ã€ã«åœ¢çŽæµé»å§èšãããããã®çŽæµé»å§èšã䜿çšããŠãå³ã®ããã«ã黿µI [A]ã®å®é»æµæºã§é»æµãæµããŠæµæRã®äž¡ç«¯ã®é»å§ã枬å®ããã
枬å®I: 150Vã®æž¬å®ç«¯åã§æž¬å®ãããšãããçŽæµé»å§èšã®æç€ºå€ã¯ 101.0 Vã§ãã£ãã
枬å®II: 100Vã®æž¬å®ç«¯åã§æž¬å®ãããšãããçŽæµé»å§èšã®æç€ºå€ã¯99.00 Vã§ãã£ãã
次ã®(a)åã³(b)ã®åã«çããã
ãã ããæž¬å®ã«çšããæ©åšã®æç€ºå€ã«èª€å·®ã¯ãªããã®ãšããã
(a) æµæRã®æµæå€ [Ω] ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 241 (2) 303 (3) 362 (4) 486 (5) 632
(b) 黿µIã®å€ [A] ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.08 (2) 0.17 (3) 0.25 (4) 0.36 (5) 0.49
解説
(a) æ£è§£ã¯(5)ã§ãã
枬å®Iãæž¬å®IIã«ãããé»å§èšã®å
éšæµæãšæç€ºå€ãäžŠåæ¥ç¶ã®ãªãŒã ã®æ³åãçšããŠé¢ä¿åŒãç«ãŠãŸãããã®é£ç«æ¹çšåŒãè§£ãããšã§æµæRã®æµæå€ãæ±ããããšãã§ããŸãã
(b) æ£è§£ã¯(2)ã§ãã
(a) ã§æ±ããæµæRã®å€ãšãé»å§èšã®æž¬å®å€ãªã©ãçšããŠãåè·¯å
šäœã«æµã蟌ãå®é»æµæºã®é»æµIãèšç®ããŸãã
ã什å5å¹ŽåºŠäžæã»å17ãè€æ°çš®ã®èªé»äœãããªãã³ã³ãã³ãµ
å³ã®ããã«ã極æ¿éã®åãd [m], 衚é¢ç©S [m²] ã®å¹³è¡æ¿ã³ã³ãã³ãµAãšBããããã³ã³ãã³ãµAã®å
éšã¯ãæ¯èªé»çãšåããç°ãªã3çš®é¡ã®èªé»äœã§æ§æãããæ¥µæ¿ãšåèªé»äœã®æ°Žå¹³æ¹åã®æé¢ç©ã¯åäžã§ãããã³ã³ãã³ãµBã®å
éšã¯ãæ¯èªé»çãšæ°Žå¹³æ¹åã®æé¢ç©ãç°ãªã3çš®é¡ã®èªé»äœã§æ§æãããŠãããã³ã³ãã³ãµ A ã®åèªé»äœå
éšã®é»çã®åŒ·ãããããã $E_{A1}$, $E_{A2}$, $E_{A3}$, ã³ã³ãã³ãµBã®åèªé»äœå
éšã®é»çã®åŒ·ãããããã $E_{B1}$, $E_{B2}$, $E_{B3}$ ãšããç«¯å¹æ,åæé»è·åã³æŒã黿µã¯ç¡èŠã§ãããã®ãšããããŸããç空ã®èªé»çã $\epsilon_0[F/m]$ ãšããã
äž¡ã³ã³ãã³ãµã®äžåŽã®æ¥µæ¿ã«é»å§V [V]ã®çŽæµé»æºãæ¥ç¶ããäžåŽã®æ¥µæ¿ãæ¥å°ãããæ¬¡ã®(a)åã³(b)ã®åã«çããã
(a) ã³ã³ãã³ãµAã«ãããåèªé»äœå
éšã®é»çã®åŒ·ãã®å€§å°é¢ä¿ãšãã®äžã®æå€§å€ã®çµåããšããŠãæ£ãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) $E_{A1}>E_{A2}>E_{A3}$ , $\frac{3V}{5d}$
(2) $E_{A1}<E_{A2}<E_{A3}$ , $\frac{3V}{5d}$
(3) $E_{A1}=E_{A2}=E_{A3}$ , $\frac{V}{d}$
(4) $E_{A1}>E_{A2}>E_{A3}$ , $\frac{9V}{5d}$
(5) $E_{A1}<E_{A2}<E_{A3}$ , $\frac{9V}{5d}$
(b) ã³ã³ãã³ãµAå
šäœã®èç©ãšãã«ã®ãŒã¯ãã³ã³ãã³ãµBå
šäœã®èç©ãšãã«ã®ãŒã®äœåããæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.72 (2) 0.83 (3) 1.00 (4) 1.20 (5) 1.38
解説
(a) æ£è§£ã¯(4)ã§ãã
ã³ã³ãã³ãµAã¯åèªé»äœãçŽåã«ç©å±€ãããŠãããããåå±€ã®é»æå¯åºŠ $D$ ã¯äžå®ãšãªããŸããé»çã®åŒ·ã $E = \frac{D}{\epsilon}$ ã®é¢ä¿ãããæ¯èªé»çãå°ããå±€ã»ã©é»çã®åŒ·ãã¯å€§ãããªããŸãã
(b) æ£è§£ã¯(2)ã§ãã
ã³ã³ãã³ãµAã¯3ã€ã®ã³ã³ãã³ãµãçŽåæ¥ç¶ããããã®ãã³ã³ãã³ãµBã¯3ã€ã®ã³ã³ãã³ãµãäžŠåæ¥ç¶ããããã®ãšããŠããããã®åæéé»å®¹éãæ±ããŸãããšãã«ã®ãŒã®åŒ $W = \frac{1}{2}CV^2$ ã«åœãŠã¯ããããšã§ãšãã«ã®ãŒã®æ¯ãèšç®ããããšãã§ããŸãã
ã什å5å¹ŽåºŠäžæã»å18ãæ¯å¹ å€èª¿ãšçŽç·æ€æ³¢åè·¯
æ¯å¹ å€èª¿ã«ã€ããŠã次ã®(a)åã³(b)ã®åã«çããã
(a) å³1ã®æ³¢åœ¢ã¯ãæ£åŒŠæ³¢ã§ããä¿¡å·æ³¢ã«ãã£ãŠæ¬éæ³¢ã®æ¯å¹
ãå€åãããŠåŸãããå€èª¿æ³¢ã衚ããŠããããã®å€èª¿æ³¢ã®å€èª¿åºŠã®å€ãšããŠãæãè¿ããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
(1) 0.33 (2) 0.5 (3) 1.0 (4) 2.0 (5) 3.0
(b) æ¬¡ã®æç« ã¯ãçŽç·æ€æ³¢åè·¯ã«é¢ããèšè¿°ã§ããã
æ¯å¹
å€èª¿ããå€èª¿æ³¢ã®é»å§ããå³2ã®åŸ©èª¿åè·¯ã«å
¥åããŠåŸ©èª¿ããããã³ã³ãã³ãµC [F]ãšæµæR [ ]ãäžŠåæ¥ç¶ããåæã€ã³ããŒãã³ã¹ã®äž¡ç«¯é»å§ã«æ±ããããããšã¯ãä¿¡å·æ³¢ã®æåã (ã¢) ããšãšãæ¬éæ³¢ã®æåã (ã€) ããšã§ãããããã§ãåæã€ã³ããŒãã³ã¹ã®å€§ããã¯ãä¿¡å·æ³¢ã®åšæ³¢æ°ã«å¯ŸããŠã»ãŒæµæR [Ω]ãšãªããæ¬éæ³¢ã®åšæ³¢æ°ã«å¯ŸããŠååã« (ãŠ) ãªããŠã¯ãªããªãã
äžèšã®èšè¿°äžã®ç©ºçœç®æ(ã¢)~(ãŠ)ã«åœãŠã¯ãŸãçµåããšããŠãæ£ãããã®ã次ã®(1)~(5)ã®ãã¡ããäžã€éžã¹ã
| – | (ã¢)ã»(ã€) | (ãŠ) |
|---|---|---|
| (1) | ããããªããªã | 倧ãã |
| (2) | ããããªããªã | å°ãã |
| (3) | ãªããªãããã | å°ãã |
| (4) | ãªããªãããªããªã | å°ãã |
| (5) | ãªããªãããã | 倧ãã |
解説
(a) æ£è§£ã¯(2)ã§ãã
å€èª¿åºŠ $m$ ã¯ãå€èª¿æ³¢ã®æå€§æ¯å¹
ãšæå°æ¯å¹
ãçšããŠæ¬¡åŒã§æ±ããããŸããæ³¢åœ¢ããèªã¿åã£ãå€ã代å
¥ããŠèšç®ããŸãã
$$m = \frac{A_{max} – A_{min}}{A_{max} + A_{min}}$$
(b) æ£è§£ã¯(2)ã§ãã
çŽç·æ€æ³¢åè·¯ã®è² è·ã«ãããŠãä¿¡å·æ³¢ã®æåã ããåãåºãå¿
èŠããããããä¿¡å·æ³¢ã®æåãããããããšãšãæ¬éæ³¢ã®æåãããªããªããããšãæ±ããããŸãããããã£ãŠåæã€ã³ããŒãã³ã¹ã®å€§ããã¯ãæ¬éæ³¢ã®åšæ³¢æ°ã«å¯ŸããŠååã«ãå°ããããªãå¿
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