Question

An LR circuit contains an inductor of $500mH$, a resistor of $25.0\Omega$ and an emf of $5.00V$ in series. Find the potential difference across the resistor at $t=\left(a\right)20.0ms$, (b) $100ms$ and(c) $1.00s$

Answer 1

$L=500mH,R=25\Omega ,E=5V$
(a) $i=i_0(1-e^{-tR/L})=\frac{E}{R}(1-E^{-rR/L})=\frac{5}{25}(1-e^{-20\times {10}^{-3}\times 25/100\times {10}^{-3}})=\frac{1}{5}(1-e^{-1})=\frac{1}{5}(1-0.3678)=0.1264$
potential difference $iR=0.1264\times 25=3.1606V=3.16V$
(b) $t=100ms$
$i=i_0(1-e^{-tR/L})=\frac{5}{25}(1-e^{-100\times {10}^{-3}\times 25/100\times {10}^{-3}})=\frac{1}{5}(1-e^{-5})=\frac{1}{5}(1-0.0067)=0.19864$
potential difference $R=0.19864\times 25=4.9665=4.97V$
(c) $t=1sec$
$=i_0(1-e^{-tR/L})=\frac{5}{25}(1-e^{-1\times 25/100\times {10}^{-3}})=\frac{1}{5}(1-e^{-50})=\frac{1}{5}\times 1=1/5A$
potential difference $iR=(1/5\times 25)V=5V$