Help with physics multiple chose questions

Question

The power dissipated in each of two light bulbs is the same. The voltage across light bulb A is twice that of light bulb B. If the resistance of light bulb B is R, what is the resistance of light bulb A?
A. R
B. 2R
C. R/2
D. 4R
E. R/4

 

The same voltage is measured across two wires. Wire A carries twice the current of wire B. If the resistance of wire B is R, what is the resistance of wire A?

A. R
B. 2R
C. R/2
D. 4R
E. R/4

Answer 1

 

P = power; V= voltage; R= resistance; I = current

 

OHM's law: V = RI

 

P = (V²)/R

 

 

FIRST PART:

 

P_A = P_B

 

V_A = 2V_B

 

P_A = (V_A)²/R_{A =} (2V_B)²/R_A

 

P_B= (V_B)²/R_B (Note: here R_B is the R in the problem, the resistance of bulb B)

 

Solve for R_A:

 

(2V_B)²/R_A = (V_B)²/R_B

 

 

SECOND PART:

 

V_A = V_B

 

I_A = 2I_B

 

Solve for R_A:

 

R_A(2I_B) = R_BI_B ((Note: here R_B is the R in the problem, the resistance of bulb B)

 

 

 

 

 

 

 

 

 

Answer 2

Part 1.

 

P_A = P_B

V_A = 2V_B

R_B = R

R_A = ?

 

P = V²/R

(2V_B)² / R_A = V_B² / R

4/R_A = 1/R

 

R_A = 4R  (answer D)

 

Part 2.

 

V_A = V_B

I_A = 2I_B

R_B = R

R_A = ?

 

I_AR_A = I_BR_B

 

R_A = I_BR_B / I_A = I_BR / (2I_B) = R/2  (answer C)