Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Strings of holiday lights can be designed in one of two ways. In so
1 answer:
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Answer:
The resonant frequency of this circuit is 14.5 kHz.
Explanation:
Given that,
Inductance of a parallel LCR circuit,
Capacitance of parallel LCR circuit,
At resonance the inductive reactance becomes equal to the capacitive reactance. The resonant frequency is given by :
or
f = 14.5 kHz
So, the resonant frequency of this circuit is 14.5 kHz. Hence, this is the required solution.
<h2>Answer:</h2>
0.46Ω
<h2>Explanation:</h2>The electromotive force (E) in the circuit is related to the terminal voltage(V), of the circuit and the internal resistance (r) of the battery as follows;
E = V + Ir --------------------(a)
Where;
I = current flowing through the circuit
But;
V = I x Rₓ ---------------------(b)
Where;
Rₓ = effective or total resistance in the circuit.
<em>First, let's calculate the effective resistance in the circuit:</em>
The effective resistance (Rₓ) in the circuit is the one due to the resistances in the two lightbulbs.
Let;
R₁ = resistance in the first bulb
R₂ = resistance in the second bulb
Since the two bulbs are both rated at 4.0W ( at 12.0V), their resistance values (R₁ and R₂) are the same and will be given by the power formula;
P =
=> R = -------------------(ii)
Where;
P = Power of the bulb
V = voltage across the bulb
R = resistance of the bulb
To get R₁, equation (ii) can be written as;
R₁ = --------------------------------(iii)
Where;
V = 12.0V
P = 4.0W
Substitute these values into equation (iii) as follows;
R₁ =
R₁ =
R₁ = 36Ω
Following the same approach, to get R₂, equation (ii) can be written as;
R₂ = --------------------------------(iv)
Where;
V = 12.0V
P = 4.0W
Substitute these values into equation (iv) as follows;
R₂ =
R₂ =
R₂ = 36Ω
Now, since the bulbs are connected in parallel, the effective resistance (Rₓ) is given by;
=
+
-----------------(v)
Substitute the values of R₁ and R₂ into equation (v) as follows;
=
+
=
Rₓ =
Rₓ = 18Ω
The effective resistance (Rₓ) is therefore, 18Ω
<em>Now calculate the current I, flowing in the circuit:</em>
Substitute the values of V = 11.7V and Rₓ = 18Ω into equation (b) as follows;
11.7 = I x 18
I =
I = 0.65A
<em>Now calculate the battery's internal resistance:</em>
Substitute the values of E = 12.0, V = 11.7V and I = 0.65A into equation (a) as follows;
12.0 = 11.7 + 0.65r
0.65r = 12.0 - 11.7
0.65r = 0.3
r =
r = 0.46Ω
Therefore, the internal resistance of the battery is 0.46Ω
Answer:
a) The swimmer should travel perpendicular to the bank to minimize the spent in getting to the other side.
b) 133.33 m
c) 53.13°
d) 106.67 m
Explanation:
a) The swimmer should travel perpendicular to the bank to minimize the spent in getting to the other side.
b) velocity = distance * time
Let the velocity of the swimmer be = 1.5 m/s
The separation of the two sides of the river, d = 80 m
The time taken by the swimmer to get to the other end of the river bank,
t = 80/1.5
t = 53.33 s
The swimmer will be carried downstream by the river through a distance, s
Let the velocity of the river be = 2.5 m/s
S = 53.33 * 2.5
S = 133.33 m
c) To minimize the distance traveled by the swimmer, his resultant velocity must be perpendicular to the velocity of the swimmer relative to water
That is ,
d) Downstream velocity of the swimmer,
The vertical displacement is given by,
80 = 1.2 t
t = 80/1.2
t = 66.67 s
the horizontal speed,
The downstream horizontal distance of the swimmer,
x = 1.6 * 66.67
x = 106.67 m