Question

3. If a certain tungsten wire has a resistance of 10.00 22 at 20.0 °C, what resistance will it have at 43.0 °C? 4. The potential difference across a resting neuron in the human body is about 75.0 mV and carries a current of about 0.200 mA. How much power (in watt) does the neuron release?

Answer 1

Ans 3: As temperature is directly propotional to the resistance. So, if temperature increases, resistance also increases.

We know that,

R=R_ref [1+$\alpha$(T-T_ref)]

where, R= Resistance of conductor at temperature "T"

R_ref= Resistance of the conductor at reference temperature =10.00$\Omega$

$\alpha$= Temperature coefficient of resistance for conductor material =0.004403 per $^{\circ}C$ for tungusten

T= Given temperature =43.0$^{\circ}C$

T_{ref =} Reference temperature = 20.0$^{\circ}C$​​​​​​​

Now putting all the values in the equation, we get,

  R=10$\Omega$[1+0.004403 (43.0$^{\circ}C$-20.0$^{\circ}C$​​​​​​​)]

=10$\Omega$[1+0.004403 $\times$ 23]

=10$\Omega$[1+0.101269]

  =10$\Omega$$\times$1.101269

=11.01269$\Omega$

Hence, the resistance will be 11.01269$\Omega$ at 43.0$^{\circ}C$

Ans 4: In the given question

V(Potential difference)= 75.0mV = 75.0$\times$ 10^-3V

I(Current)= 0.200mA = 0.200$\times$ 10^-3A

We know that,

P(Power) =V(Potential difference)$\times$I(Current)

Putting the values in given equation

P = 75.0$\times$ 10^-3V$\times$0.200$\times$ 10^-3A

=15 $\times$ 10^-6 W

=0.000015 W

Hence the neuron releases 0.000015 W power.