The figure below shows a circuit with two identical resistors and an ideal conductor Is the current through the central resistor more than, less than, or the same as that through the other resistor (a) just after the closing of switch S, (b) a long time after that, (c) just after S is reopened a long time later, and (d) a long time after that? You must justify your answers.
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- Check Your Understanding When using Kirchhoff’s laws, you need to decide which loops to use and the direction of current flow through each loop. In analyzing the circuit in Example 10.7, the direction of current flow was chosen to be clockwise, from point a to point b. How would the results change if the direction of the current was chosen to be counterclockwise, from point b to point a?The timing device in an automobile's intermittent wiper system is based on an RC rime constant and utilizes a 0.500F capacitor and a variable resistor. Over whatrange must R be made to vary to achieve time constants from 2.00 to 15.0 s?Consider the circuit shown below. Find l1, l2and l3when (a) the switch S is first closed, (b) after the currents have reached steady-state values, and (c) at the instant the switch is reopened (after being closed for a long time).
- in the circuit shown in the figure, the S switch is closed at t=0 and the capasitors, which are completely empty, begin to fill. Here E=30V, C=3 uF and R=40 ohm. A) what is the time constant of the circuit, T, in the units of microseconds? B)when t=T, what is the total charge, in units of microcoulomb?The equation P= V2/R indicates that the power dissipatedin a resistor decreases if the resistance is increased, whereasthe equation P=I2R implies the opposite. Is there acontradiction here? Explain.In the first two parts of this experiment, we observe that when we flip the switch, thevoltage first very quickly changes to one value, then slowly changes after that. Let's examinehow to explain this.● Suppose the wire has a 10Ω resistance (which is almost certainly an overestimate) andthe voltmeter has a 1MΩ resistance (1Ω=1s/F). Given that our capacitances are of order~10μF, compute the time constant for each resistance: this is essentially the time it takesfor current to "go through" that component. From these timescales, consider: of the twoprocesses described above (the quick change in voltage and the slow change in voltage),which process is controlled by each component's resistance?
- A capacitor, C, is (fully) charged by connecting it to a 7 Volt EMF and then is allowed to dischargethrough a 2 Ω resistor as shown in the Figure. What is the current, I, in the circuit (in A) when thestored energy in the capacitor has dropped to 30% of its initial value?The remaining circuit quantities may change instantaneously as required by Kirchhoff's rules. Calculate I2 in amps immediately after the switch (t = 0+), in that order. (All currents in this and the following two should be positive.)A bank of batteries, total emf ε = 4.5 V, is connected with resistor R = 120 kΩ, capacitor C = 680 pF, and two-pole switch S as shown. The switch is initially set to point b so that the resistor and capacitor are in series. The switch is left in this position for a sufficiently long time so that the capacitor is completely discharged. Calculate the voltage drop across the capacitor (in volts) at time t = 210 μs after the switch is connected to point a.
- All the capacitors shown are completely charged. When the switch is closed (assume at t = 0 s), at what time has the current in the 8 Ω resistor decayed to half its original value?The magentic field through a single loop of wire 16.0 cm in radius and of 8.5 ohm resistance changes with time as shown in the figure. Calculate the emf in the loop as a function of time. What is the emf at t=5.0 s? What is the current at t= 1.0 s?Imagine a hypothetical universe where Ohm's law still holds true, but the nature of matter allows for electrical resistors to possess negative resistance values. In such a universe, how would the rules for combining resistors in series and parallel change? Furthermore, how could this altered physics influence the functioning of basic electrical circuits and energy conservation principles?