Four resistors are connected together in the configuration shown in the figure b

Question

Four resistors are connected together in the configuration shown in the figure below. A battery is connected to this set of resistors so that its positive terminal is connected by a wire to one of the lettered points, and the negative terminal is connected to another of the lettered points. Consider the following three cases. 1: Positive terminal connected to a; negative terminal to b 2: Positive terminal connected to a; negative terminal to c 3: Positive terminal connected to b; negative terminal to c

http://tinypic.com/r/2e4i4hj/5

(a) Rank these cases, from largest to smallest, based on their equivalent resistance.

(b) Rank these cases, from largest to smallest, based on the magnitude of the current through the 4-ohm resistor.

(c) Rank these cases, from largest to smallest, based on the magnitude of the potential difference across the 8-ohm resistor.

Explanation / Answer

let battery connected is of V volts case 1: when +ve is connected to a and -ve to b Req = 1.7 ohms current through 4 ohms = V/12 = 0.08V Amperes potential difference across 8 ohms resistor = 14V/3 = 4.66V Volts case 2: when +ve is connected to a and -ve to c Req = 3.4 ohms current through 4 ohms = 7V/30 = 0.23V Amperes potential difference across 8 ohms resistor = V Volts case 3: when +ve is connected to b and -ve to c Req = 2.8 ohms current through 4 ohms = 7V/28 = 0.25V Amperes potential difference across 8 ohms resistor = 4V/7 = 0.57V Volts (a) on the basis of equivalent resistance 1 < 3 < 2 (b) on the basis of current through 4 ohms resistor 1 < 2 < 3 (c) on the basis of voltage across 8 ohms resistor 3 < 2 < 1

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