Because R1 and R2 are expressed in the same units, the equation R1/R2 becomes a simple multiplication factor. This equation provides a numerical value for C_x and will be in the same units as C _s (farad, microfarad, and so forth).

Similarly, the following resistance ratio exists between the four arms of the bridge, just as in the resistance bridge expression discussed earlier:

or

Thus, both the unknown resistance and capacitance, R _x and C_x, can be estimated in terms of known resistance R1, R2, R_s, and known capacitance C _s.

In figure 1-7, for example, we know that R1 is 20 ohms, R2 is 40 ohms, R_s is 60 ohms, and C _s is 10 microfarads. We can find the values of C_x and R_x by using the respective formulas as follows:

and

Q.19 When a bridge is used to measure resistance, what is the value of R_x if R1 equals 80 ohms, R2 equals 120 ohms, and R3 equals 280 ohms?

INDUCTANCE BRIDGE. - The value of the unknown inductance L_x may be determined by means of the simple bridge circuit shown in figure 1-8. Ratio arms R1 and R2 are accurately calibrated resistors. L_s is a standard inductor with a known inductance; R_s is the known resistance, and R_x represents the resistance of the unknown inductor.

Figure 1-8. - Inductance bridge.

The ac signal is applied to the bridge, and variable resistors R1 and R2 are adjusted for a minimum or zero deflection of the meter, indicating a condition of balance. When the bridge is balanced, the following formulas may be used to find L_x.

(NOTE: The right side of this expression is NOT inverse as it was in the capacitance bridge.)

and

or

In figure 1-8, for example, the values of R1, R2, and R_s are 20, 40, and 60 ohms, respectively. The value of L_s is 10 millihenries. We can find the values of R_x and L_x by using their respective formulas as follows:

and

Thus, both the unknown resistance and inductance can be estimated in terms of the known values for R1, R2, R_s, and L _s.

Q.20 When an unknown capacitance is tested with a bridge, what is the value of C_x if R1 equals 70 ohms, R2 equals 150 ohms, and C_s equals 550 microfarads?