I. Let ω and η be 1-forms in R3 given by a) Compute dn b) Evaluate doAn
Let ω be a k-form and let η be a 1-form. Find d(don η-ω^ dn)
RA b R3 a 20 Ω 8 Ω 1, 12 IS 6Ω 0.5 Ω R2 E3 12V Ε, 18V Ε. g 3.0V 0.5 Ω ω Γ2 0.25 Ω EA RA f - D 15 Ω 0.75 Ω 24V For the circuit given above, calculate V-Vd Answer:
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
Please show each step of the problem so I can
understand
Η 1ο Ε = 6.0ν 4. Determine the each of the currents in each path, and the voltages across each resistor. Ε, = 24.0ν b d 0.10Ω R RS 5.0Ω E = 48.0ν 20 Ω Γ2 k R2 a 15 0.50 Ω 40 Ω 0.20 Ω R3 78 Ω Ε. = 36.0ν Γ3 g Η e Έ 10.05 Ω h
answers in rectangular and polar forms
Given that Evaluate a. A+B C b. A+ A+B
In the circuit shown in (Figure 1), R1=3 Ω , R2=5 Ω , R3=4 Ω ,
R4=9 Ω , and R5=9 Ω .
Part A: What is the current flowing through resistor R1 (A)?
Part B: What is the current flowing through resistor R2
(A)?
Part C: What is the current flowing through resistor R3 (A)?
Part D: What is the total power supplied by the battery (W)?
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In the figure R1 = 100 Ω,
R2 = R3 = 49.0 Ω,
R4 = 67.5 Ω, and the ideal battery has emf ε =
6.00 V. (a) What is the equivalent resistance?
What is i in (b) resistance 1,
(c) resistance 2, (d) resistance
3, and (e) resistance 4?
5a. Let (and nyl be the sequence given by An= 5nt - dn t 3 No ů What is the limit of can)? (1) Prove your answer in ) using the definition of the limit of a sequence : b. het (Audna, be a sequence ce of real numbers. In each of the following cases, check if the sequence Cand is a cauchy sequence. Justify your answers is an on 5 มาก
In the figure R1 = 120 Ω,
R2 = R3 = 43.0 Ω,
R4 = 106 Ω, and the ideal battery has emf ε =
6.00 V. (a) What is the equivalent resistance?
What is i in (b) resistance 1,
(c) resistance 2, (d) resistance
3, and (e) resistance 4?
R RA + 18 R2 RS
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify your answer. iii. Find a function y: R3-+ R such that F iv. Evaluate F.dr where「is the path y =r', z = 0, from (0.0.0) to (2.8.0) followed by the line segment from (2,8,0) to (1,1,2) 22 marks)
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3),...