Two single-core power cables have total conductor resistance of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ______ × 10⁶.

The correct answer is 300.

When two single-core power cables are joined in series, we calculate the equivalent conductor resistance and the equivalent insulation resistance as follows:

1. Total Conductor Resistance ($R_{\text{conductor}}$):
Since the conductors of the two cables are joined in series, their individual conductor resistances are in series and simply add up:
$R_{\text{conductor}}=0.7\Omega +0.5\Omega =1.2\Omega$

2. Total Insulation Resistance ($R_{\text{insulation}}$):
Insulation resistance is measured between the core (conductor) and the sheath. When the cables are connected in series, the paths for current leaking from the core to the sheath in both cables act in parallel. Therefore, the equivalent insulation resistance is the parallel combination of the individual insulation resistances:
$R_{\text{insulation}}=\frac{600\times 900}{600+900}=\frac{540000}{1500}=360M\Omega$
In ohms, this is:
$R_{\text{insulation}}=360\times {10}^6\Omega$

3. Ratio of Insulation Resistance to Conductor Resistance:
The ratio is given by:
$\frac{R_{\text{insulation}}}{R_{\text{conductor}}}=\frac{360\times {10}^6}{1.2}=300\times {10}^6$

Therefore, the value to fill in the blank is 300.