Question

You are given a semiconductor resistor made from silicon with an impurity concentration of resistivity 1.00×10−3ωm. the resistor has a height of h =0.5 mm, a length of l = 2 mm, and a width of w = 1.25 mm. the resistor can absorb (dissipate) up to p = 7.81w. what is the resistance of the resistor (r), the maximum voltage (v), and the maximum current (i)?

Answer 1

Answer: Resistance =$3.2 \Omega$ , Current = 1.56 A, Voltage =4.99 V

The resistance,

$R=\frac {\rho l}{A}$

where, $\rho$ is resistivity, A is the area and l is the length of the resistor.

It is given that:

$\rho=1.0\times10^{-3}\Omega m$

Length, l=2 mm

Area, $A= width \times height=1.25 mm\times 0.5 mm=0.625 mm^2$

Hence, $R=\frac{1.0\times10^{-3}\Omega m \times 2\times10^{-3}m}{0.625\times10^{-6}m^2}=3.2\Omega$

We know, Power, $P=I^2R$

$\Rightarrow I=\sqrt{\frac{P}{R}}$

$P=7.81 W$

$I=\sqrt{\frac {7.81 W}{3.2\Omega}}=\sqrt{2.44}A=1.56A$

We know, Voltage, $V=IR=1.56\times3.2=4.99 V$