capacitor discharge calculator shell script

capacitor.sh

#!/bin/zsh -f
# capacitor discharge - scruss, 2023-11
#  - this should work with bash too but the formatting may be off
#  - weird narrow format was designed for thermal printer output

if
    [ "$#" -lt 3 ]
then
    echo "usage: $0 resistance capacitance voltage [V₀]"
    exit 1
fi

echo ''
printf '%10s%10s\n' 'Capacitor' 'Discharge'
printf '%10s%10s\n' '*********' '*********'
echo ''

r="$1"
printf '%-9s:%10.3G\n' 'R    / Ω' "$r"
c="$2"
printf '%-9s:%10.3G\n' 'C    / F' "$c"
v="$3"
printf '%-9s:%10.3G\n' 'V    / V' "$v"

v0=""
# pick up v0 if we have it
if
    [ "$#" -gt 3 ]
then
    v0="$4"
    printf '%-9s:%10.3G\n' 'V₀   / V' "$v0"
fi

# time constant
tau=$(echo "$r * $c" | bc -l)
printf '%-9s:%10.3G\n' 'τ    / s' "$tau"
# initial (max) power
pmax=$(echo "${v}^2 / $r" | bc -l)
printf '%-9s:%10.3G\n' 'Pmax / W' "$pmax"
echo ''
printf '%10s%10s\n' 'Time / s' "Volts / V"
printf '%10s%10s\n' '=========' '========='


for i in {0..5}                  
do
    t=$(echo "$i * $tau" | bc -l)
    v1=$(echo "$v * ( 1 / e(1)^$i )" | bc -l)
    printf '%10.3G%10.3G\n' "$t" "$v1"
done
echo ''

if
    [ ! -z "$v0" ]
then
    t0=$(echo "$tau * l( $v / $v0 )" | bc -l)
    printf '%-9s:%10.3G\n' 'V→V₀ / s' "$t0"
    echo ''
fi