The resistors Ra and Rb are connected in series across a 120 volt source.?

Question

The resistors Ra and Rb are connected in series across a 120 volt source. When a 30,000 ohms voltmeter is connected across Ra and then across Rb, the instrument deflection is 48 volts in each case. What are the values of the resistors?

Answer 1

The resistors are equal, and each has 60 volts across it with the meter missing.

It = total current with meter connected

Im = current through meter

Im = 48/30k = 1.6ma

It = 72v/R (unbridged R)

R = 72/It

R = 48/(It-1.6ma) (R with meter)

72/It = 48/(It-1.6ma)

72*(It-1.6ma) = 48*It

72It - 115.2m = 48*It

24It = 115.2m

It = 4.8 ma

R = 72/4.8 = 15k

check

15k parallel 30k = 10k

total I, with meter = 120/(15k+10k) = 4.8ma

drop across 10k = 48v

.

Answer 2

first of all u can say the resistors are identical because the voltmeter deflection is the same for both.

2nd, u know when connected in series, the ratio of voltages of resistors is equal to the ratio of their values of resistance. (V2/V1=R2/R1).

and 3rd, u know when connected in parallel, the equivalent resistance is R1R2/(R1+R2).

now u have this equation: 48/(30000R/(R+30000))=72/R.

solving for R yields: R = 15000 Ohms ans