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deff fn [24]
3 years ago
7

Which do we do to find the equivalent of resistors in parallel?

Physics
1 answer:
Roman55 [17]3 years ago
6 0

Answer:

We sum the inverse of each resistance and then invert the sum.

Explanation:

The equivalent resistance in case of parallel combination of resistors is given by the formula as :

\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}

Here,

R is the equivalent resistance

R_1\ and\ R_2 are individual resistors that are connected in parallel

We can find the value of R as :

  • Firstly, we add the inverse of the individual resistances.
  • Secondly, we invert the sum that we get in above step.

So, the correct option is (a) "We sum the inverse of each resistance and then invert the sum".

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Answer:

a. B= 9.45 \times10^{-3} T

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Explanation:

First, look at the picture to understand the problem before to solve it.

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B=\frac{u_{0}I_{w}}{2\pi d_{1}} =\frac{52 \times4\pi \times10^{-7} }{2\pi 1.1 \times 10^{-3}} =9.45 \times10^{-3} T\\

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b. d2=3.6 mm

Here, the point is located in the surface of the cilinder. Therefore, we have to consider the current density of the conductor to calculate the magnetic field as follows:

J: current density

c: outer radius

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The cilinder's current is negative, as it goes on opposite direction than the wire's current.

J= \frac {-I_{c}}{\pi(c^{2}-b^{2}  ) }}

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B=\frac{u_{0}(I_{w}-JA_{s})}{2\pi d_{2} } \\A_{s}=\pi (d_{2}^{2}-b^2)=4.40\times10^{-6} m^2\\

B=\frac{6.68\times10^{-5}}{8.14\times10^{-5}} =0.820 T

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Here, the point is located out of the cilinder. Therefore, we have to consider both, the conductor's current and the wire's current as follows:

B=\frac{u_{0}(I_w-I_c)}{2\pi d_3 } =\frac{2.011\times10^-5}{3.441\times10^{-4}} =0.0584 T

As we see, the magnitud of the magnetic field is greater inside the conductor, because of the density of current and the material's nature.

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