Suppose a multimeter is used to measure voltage differences

Suppose a multi-meter is used to measure voltage differences in the circuit below, represented as a schematic diagram. Suppose the battery is 10 Volts and each resistor is 47 mega Ohms. Without applying the meter, what should be the voltage difference between points b and c? If you want to measure the voltage difference from point b to point a (a positive value) where would you connect the V ohm. wire and where would you connect the COM wire? Indicate these connections with lines. Now suppose you actually make this measurement and find V_a - V_b = 4.89 Volts. What is the resistance of the volt meter? (Actually, the effective volt-meter resistance will depend on which scale you have it set to, so this would be for a particular meter setting.)

Solution

a)

R_total = total resistance of the circuit = 47 + 47 = 94 ohm

i = current in the circuit

i = V/R_total = 10/94 = 0.11 A

V_bc = i R = 0.11 x 47 = 5.2 volts

b)