The total resistance R of three resistors in parallel is given by RR,R3 R = R,R2+R,R3+R,R3 Suppose that a 6 -2 and a 12 -2 resistor are placed in parallel with a variable resistor of resistance x.
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The total resistance R of three resistors in parallel is given by......
Write R as a function of x.
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- (a) Suppose two resistors are connected in parallel with resistances Rị and R2 measured in Ohms (N). The total resistance R is given by 1 1 1 R R1 R2 Suppose R1 is increasing at a rate of 1/4 2/s and R2 is increasing at a rate of 1/16 N/s. At what rate is R changing when R1 = 1/2 N and R2 = 1/4 N. (b) Car A is traveling North at a rate of 60 mi/hr, car B is traveling West at a rate of 45 mi/hr. The cars are on straight roads approaching an intersection point. At what rate is the distance between the cars changing when Car A is 3 miles from the intersection and Car B is 4 miles from the intersection.Prove that when n identical resistors of resistance R are connected in parallel the equivalent resistance is R/n.A 6-mF capacitor is charged to 12 V and then connected across a 100 W resistor. Find (a) The initial charge on the capacitor (b) The initial current through the resistor (c) The time constant (d) The charge on the capacitor after 3 ms
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- An uncharged capacitor and a resistor are connected in series to a source of emf. If = 8.00 V, C = 25.0 µF, and R = 100 Ω, find the following. (a) the time constant of the circuit Your response is off by a multiple of ten. ms(b) the maximum charge on the capacitor µC(c) the charge on the capacitor at a time equal to one time constant after the battery is connected µCA 20-Ω resistor is connected to four 1.5-V batteries. What is the joule heat loss per minute in the resistor if the batteries are connected … (a) in series and … (b) in parallel?A thermistor is a type of resistor whose resistance varies significantly with temperature, more than in standard resistors. Thermistors are widely used as inrush current limiter, temperature sensors (NTC type typically), self-resetting overcurrent protectors, and self-regulating heating elements. Assume that the relation between resistance (R) in ohms and temperature (T) in Celsius of the thermistor is given by: R=(1+0.3T)/2 By using error propagation formula, calculate the temperature and associated error if R = 15 ± 1 Ω.
- If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R, measured in ohms (Ω), is given by 1/R =1/R1 + 1/R2. If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast (in Ω/s) is R changing when R1 = 80 Ω and R2 = 100 Ω?In an experiment, an initially uncharged capacitor of capacitance C=62µF (microFarad) is connected to a resistor R and a battery of voltage V as shown in the figure below: V(V) VT After the switch is closed at t=0, the voltage across the capacitor is measured and plotted as shown in the figure below. Using the data provided in the curve, determine the value of resistance R. Express your answer in units of using zero decimal places. 13- 12- 11 10- 9 8- 7- 6 5 4- 3 2 1- 0- 0 P 0.1 66****** 0.2 0.3 R www 0.4 0.5 C 0.6 t (s) 0.7 0.8 0.9 1 1.1 1.2 4An engineer fashions an 3.9-k equivalent resistor from a parallel combination of 4 equal- value resistors. What is the resistance (in kQ) of each individual resistor?