Q7: Series and Parallel DC Circuits

In the circuit shown in Fig 7 find the total resistance RT with terminals a and b (a)open-circuited, and (b) short-circuited.

With terminal a and b open, the 20 and 90 ohm resistors are in series, as are 60 and 10 ohm resistors. The two series combinations are in parallel; so

RT = (20 + 90) * (60 + 10) / (20 + 90) + (60 + 10)

For terminal a and b short-circuited, the 20 and 90 ohm resistors are in parallel, as are 60 and 10 ohm resistors. The two parallel combinations are in series,making

RT = (20 + 90) / (20 + 90) + (60 * 10) / (60 + 10)

Book reference:John O’Malley Basic Circuit Analysis 2011 p44, McGrowHill