Section 3 40 2 1O O 107 48 (a) What is the equivalent resistance of this circuit

Question

Section 3 40 2 1O O 107 48 (a) What is the equivalent resistance of this circuit? That is, what would be the resistance of a single resistor that would draw the same current and power as this circuit does? Answer: (b) What is the current in resistor "K”? (That is, the one whose value comes from column K in the spreadsheet?) Answer: (c) What is the potential drop (voltage) across resistor "M"? Answer: (d) How much power is being delivered to resistor "N"? Answer: (e) What is the current in resistor “O"? Answer:

Explanation / Answer

a) Effective resistance of resistors r1 and r2 in parallel, R is given by
1/R = 1/r1 + 1/r2
Effective resistance of resistances r1 and r2 in series, R is given by
R = r1 +r2
Resistances M and N are in parallel. Effective resistance, of M and N, R1 is given by
1/R1 = 1/44 + 1/42 => R1 = 21.5
R1 and O are in series. Effective resistance, of O and R1, R2 is given by
R2 = 21.5 + 107 = 128.5
R2 and K are in parallel. Effective resistance, of R2 and K, R3 is given by
1/R3 = 1/128.5 + 1/10 = 9.3
R3 is in series with J and L. Hence equivalent resistance of circuit
R = 9.3 + 70 + 48 = 127.3 ohm

b) When resitors are in series, potential drop across resistors is proportional to the ressitance.
R3 , J and L are in series with total potential drop = 75 V
Potential drop across R3 = 9.3*75 / (127.3) = 5.5V
R3 , consist of K and R2 in parallel. Hence potetial drop across K = 5.5 V
Current through K = potential drop across k / resistance of K = 5.5/10 = 0.55 Amp

c) R1 and O are in series, with total potential drop = 5.5 V
so potetnial drop across R1 = 21.5*5.5 / 128.5 = 0.9 V
R1 is resistance of M and N in parallel, so potential drop across M = potential drop across N = 0.9

d) Power delieverd to resistor = V2 / R ( V is potential drop across resistor)
power delieverd to N =  0.92 / 44 = 0.02 W

e) R1 and O are in series. current through R1 = current through O
potetial drop across R1 = 0.9 and R1 = 21.5
current through R1 or O = 0.9/21.5 = 0.04 Amp

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