The figure shows a simple RC circuit consisting of a 100.0−V battery in series with a 10.0−μF capacitor and a resistor. Initially, the switch S is open and the capacitor is uncharged. Two seconds after the switch is closed, the voltage across the resistor is 37 V. (i). Calculate the numerical value of R. (ii). Calculate the amount of charge on the capacitor 2.0 s after the switch is Closed.
Symbolic Solve: A rod of finite length L and a negative charge −Q distributed throughout is bent into an arc. a. Derive an expression for the magnitude of the electric field at point O. b. Using your expression from part A, let Q = −7.5 μC and L = 14.0 cm, and calculate the magnitude of the electric field. c. What direction does the E-field point at point O?
A thin, semicircular wire of radius R is uniformly charged with total positive charge Q (see figure below). Determine the electric field at the midpoint O of the diameter. (Use any variable or symbol stated above along with the following as necessary: k.) magnitude E = direction
Check the divergence theorem for the vector function A = s2 Sin[φ]s^ + 2s2 Cos[φ]φ^ + 3szSin[φ]z^ (cylindrical coordinates) using the volume of a half-cylinder as shown in the figure. The base of the half cylinder is in the x−y plane (z = 0) and the vertical plane is in the x−z plane (y = 0). The radius of the cylinder is R and the height is L.
Tthree point charges, Q1 = 12.4 μC, Q2 = −30.6 μC, and Q3 = 57.3 μC are positioned at three corners of a square as shown in the figure. A fourth point charge is located at the open corner at point A with a charge of QA = 17.5 μC. The square has height y of 80.1 cm and width x of 80.1 cm.
Four point-like charges are placed as shown in the figure, three of them are at the corners and one at the center of a square, 24.0 cm on each side. What is the electric potential energy of the entire system of charges? Let q1 = +13.0 μC, q2 = −32.0 μC, q3 = +24.0 μC, and q4 = −47.0 μC. J
For the circuit in the given figure, determine the current IR. Let RB = 30 kΩ, RC1 = 1 kΩ, RC2 = 3 kΩ, R = 27 kΩ, VBB1 = 4 V, VBB2 = 3 V, VCC = 10 V, β1 = 40, and β2 = 60. The current IR is μA.
You have available two resistors having values exactly 470 Ω and 1.0 kΩ respectively, and a +3.0 V supply. You must use only these to produce the closest you can to +1.0 V output. Draw the circuit diagram, and calculate the actual voltage produced. Which resistor must be shunted (paralleled) by a third resistor to produce exactly +1.0 V output? What is the value of that third resistor? Calculate the power dissipation in each of the three resistors individually, when nothing is connected to the circuit output.
We wish to replace the circuit below with its Norton equivalent. All resistors are the same, R = 4.3 kΩ. The dependent current source is controlled by vx as shown, where G = R-1 = (4.3 kΩ)-1 = 0.23256 μs. The voltage source is V = 8 V. The short circuit current between terminals A and B is isc = mA. The equivalent resistance between terminals A and B is Req = kΩ.
A series AC circuit contains a resistor, an inductor of 230 mH, a capacitor of 5.50 μF, and a source with ΔVmax = 240 V operating at 50.0 Hz. The maximum current in the circuit is 190 mA. (a) Calculate the inductive reactance. Ω (b) Calculate the capacitive reactance. Ω (c) Calculate the impedance. kΩ (d) Calculate the resistance in the circuit. kΩ (e) Calculate the phase angle between the current and the source voltage.
You are working in a factory and have been tasked with determining the electrical needs for a new motor that will be installed on an assembly line. The motor has been tested under load conditions and found to have a resistance of 39.0 Ω and an inductive reactance of 49.0 Ω. We can model the motor as a series RL circuit. The motor will have its own dedicated circuit with an rms voltage of 450 V. You need to determine the peak current (in A) drawn by the motor to determine the size of the circuit breaker needed to protect the circuit. A
Consider a sensor interface circuit consisting of a thermistor (represented by the variable resistor RX) connected to a 10-bit ADC, as shown below. The parameters of the circuit are: VS = 10 VR = 2.7 kΩ If the variation of RX is from 3.2 kΩ ≤ RX < 7.4 kΩ, what is the range of input voltage (vIN ) to the ADC? V ≤ VIN < V A 10-bit ADC is chosen such that the reference voltage VREF of the ADC is 10 V. What is the voltage resolution of the ADC? mV If the resistance of the thermistor corresponding to the temperature of a room is 4.9 kΩ, determine the following: vIN = V output of the ADC, D9 D8 D7 D6 D5 D4 D3 D2 D1 D0 =
An AC source operating at 57 Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and an inductor (L = 2.1 H). (a) What is the maximum value of the current in the circuit? A (b) What are the maximum values of the potential difference across the resistor and the inductor? ΔVR,max = V ΔVL,max = V (c) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the inductor, and the AC source? ΔvR = V ΔvL = V Δvsource = V (d) When the current is zero, what are the magnitudes of the potential difference across the resistor, the inductor, and the AC source? ΔvR = V ΔvL = V Δvsource = V
The parameters of all elements in the circuit shown below are given: R1 = 13.6 kΩ, R2 = 2.3 kΩ, R3 = 4.2 kΩ, C = 3.92 μF, and ε = 5.7 V (the internal resistance of the battery is negligible). The capacitor in this circuit is not charged when, at time t = 0, the switch S 1 is closed. Then, at time t = 47.28 ms, the switch S 2 is closed. What is the charge Q(t) on the capacitor at time t = 63.33 ms: Q(t) = μC. What is the current I2(t) in resistor R2 at time t = 63.33 ms: I2(t) = mA
The circuit shown below on the left has the following parameters: IS = 3 mA R1 = 6.8 kΩ R2 = 3.3 kΩ R3 = 3.9 kΩ This circuit is to be replaced by an equivalent one shown on the right, such that the voltage and current 'received' by an arbitrary load resistor RL are identical when connected to either circuit. Determine the value of the voltage source VX and the resistor RX in the equivalent circuit.
Consider the given circuit where I1 = 3.000 A and RX = 5.00 Ω. Employ superposition to determine the individual contribution from each independent source to the current ix as labeled in the given circuit. (Round the final answer to three decimal places.) The value of current ix is A. The contribution of the 3.000 A current source to ix is A. The contribution of the 2 V voltage source to ix is A.