For the circuit shown below,write the equations for the three loops by using Kirchhoff's loop rule.

(N/A) Applying Kirchhoff's loop rule (sum of potential changes around a closed loop is zero):
For loop $ahdcba$:
Starting from $a$ and moving clockwise: $-30 I_{1} + 45 - 1 I_{3} - 40 I_{3} = 0$
$\therefore -30 I_{1} - 41 I_{3} + 45 = 0 \quad \ldots (1)$
For loop $ahdefga$:
Starting from $a$ and moving clockwise: $-30 I_{1} + 20 I_{2} + 1 I_{2} - 80 = 0$
$\therefore -30 I_{1} + 21 I_{2} - 80 = 0 \quad \ldots (2)$
For loop $bcdeab$:
Starting from $b$ and moving clockwise: $40 I_{3} + 1 I_{3} - 45 + 20 I_{2} + 1 I_{2} = 0$
$\therefore 41 I_{3} + 21 I_{2} - 45 = 0 \quad \ldots (3)$