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A carbon resistor is 5 mm long and hasa constant cross section of 0.5mm2. The conductivity of carbon at room temperature is = 3104 per ohm·m. In a circuit itspotential at one end of the resistor is 13 volts relative to ground, and at the other endthe potential is 17 volts. Calculatethe resistance R and the current I.R = .333correct check mark0.333I =12.01amperesexplane how to work this problem with the actualwork.

1 Answer

4 votes

Step-by-step explanation:

The given data is as follows.

l = 5 mm =
5 * 10^(-3) m, A = 0.5
mm^(2) =
0.5 * 10^(-6) m^(2)

conductivity (
\sigma) =
3 * 10^(4) per ohm-m


V_(1) = 13 volts,
V_(2) = 17 volts

Now, the relation between conductivity and resistivity is as follows.


\sigma = (1)/(\rho)

where,
\rho = resistivity

Therefore, calculate resistivity as follows.


\sigma = (1)/(\rho)


\rho = (1)/(3 * 10^(4))

=
3.33 * 10^(-5) ohm-m

Now, we will calculate the resistance using the following formula.

R =
\rho (l)/(A)

=
3.33 * 10^(-5) ohm-m * (5 * 10^(-3) m)/(0.5 * 10^(-6) m^(2))

= 0.333 ohm

Hence, value of resistance is 0.333 ohm.

As we know that relation between current and voltage is as follows.

V = IR

Therefore, calculate the value of current as follows.

V = IR

(17 - 13) =
I * 0.333 ohm

I = 12.01 ampere

Thus, value of the current is 12.01 A.

User Pravdomil
by
8.3k points
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